tag:blogger.com,1999:blog-86332425664338117022023-11-16T08:02:17.112-08:00FISICA. I Bloque 2Karlahttp://www.blogger.com/profile/05031254835401085216noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8633242566433811702.post-87128267629228102792009-11-12T20:25:00.001-08:002009-11-12T20:25:28.862-08:00<span xmlns=''><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><div><table border='0' style='border-collapse:collapse'><colgroup><col style='width:192px'/><col style='width:192px'/><col style='width:192px'/></colgroup><tbody valign='top'><tr style='background: yellow'><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:18pt'><strong>Magnitud</strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='font-family:Arial; font-size:18pt'><strong>Nombre<br /></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='font-family:Arial; font-size:18pt'><strong>Símbolo</strong></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Superficie</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro cuadrado</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m2<br /></span></p></td></tr><tr style='background: #92d050'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Volumen</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro cúbico</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m3<br /></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Velocidad</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro por segundo</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m/s<br /></span></p></td></tr><tr style='background: #92d050'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Aceleración</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro por segundo cuadrado</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m/s2<br /></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Número de ondas</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro a la potencia menos uno</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m-1</span></p></td></tr><tr style='background: #92d050'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Masa en volumen</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>kilogramo por metro cúbico</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>kg/m3<br /></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Velocidad angular</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>radián por segundo</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>rad/s<br /></span></p></td></tr><tr style='height: 38px'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:18pt'><strong>MAGNITUD</strong></span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:18pt'><strong>SI</strong></span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:18pt'><strong>CGS</strong></span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:18pt'><strong>INGLES</strong></span></p></td></tr><tr style='height: 22px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Longitud</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Metro (m)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Centímetro(m)<br /></span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie</span></p></td></tr><tr style='height: 22px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Masa</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Kilogramo (kg)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Gramo (g)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Libra</span></p></td></tr><tr style='height: 32px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Tiempo</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Segundo (s)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Segundo (s)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Segundo (s)</span></p></td></tr><tr style='height: 27px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Área</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Cm2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie2</span></p></td></tr><tr style='height: 26px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Volumen</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>M3</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Cm3</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie3</span></p></td></tr><tr style='height: 32px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Velocidad</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m/s</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Cm/s</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie/s</span></p></td></tr><tr style='height: 28px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Aceleración </span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m/s2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Cm/s2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie/s2</span></p></td></tr><tr style='height: 27px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Fuerza</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Kgm/s newton</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>gcm/s2=dina </span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Librapie/s2=potencial</span></p></td></tr><tr style='height: 28px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Trabajo</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Nm=joule</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Dina cm=baria</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Poental/pie2</span></p></td></tr><tr style='height: 26px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Energía</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Nm=joule</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Dina cm=baria</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Poental/pie</span></p></td></tr><tr style='height: 15px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Presión </span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>n/m2=pascal</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Dina/cm2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Poental pie</span></p></td></tr><tr style='height: 21px'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>potencia</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center; background: #ff3399'><span style='color:black; font-family:Arial; font-size:14pt'>Joule/swatt</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center; background: #ff3399'><span style='color:black; font-family:Arial; font-size:14pt'>Ergio/s</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center; background: #ff3399'><span style='color:black; font-family:Arial; font-size:14pt'>Poental pie/s</span></p></td></tr></tbody></table></div><p><br /> </p><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:14pt'>CONVERSIONES<br /></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:14pt'>TIPO DE VECTORES<br /></span></p><p><br /> </p><div><table border='0' style='border-collapse:collapse'><colgroup><col style='width:153px'/><col style='width:213px'/><col style='width:208px'/></colgroup><tbody valign='top'><tr style='height: 47px; background: #d6e3bc'><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><strong>TIPO DE VECTOR</strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><strong>DEFINICIÒN</strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><strong><em>REPRESENTACIÒN</em></strong></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong> Colineal</strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Son aquellos vectores que están contenidos<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>en una misma línea de acción.<br /></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p style='text-align: center'/></td></tr><tr style='background: #d6e3bc'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p> <br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong><em>Concurrente</em></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Son aquellos vectores cuyas líneas de acción,<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>se cortan en un solo punto.<br /></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'/></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong><em>Coplanar</em></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Son aquellos vectores que están contenidos<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>en un mismo plano.<br /></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'/></td></tr><tr style='background: #d6e3bc'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong><em>Iguales</em></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Son aquellos vectores que tienen la misma<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>intensidad, dirección y sentido</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'/></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong><em>Opuesto</em></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Se llama vector opuesto (-A) de un vector A<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>cuando tienen el mismo módulo, la misma dirección,<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>pero sentido contrario.<br /></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'/></td></tr></tbody></table></div><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong>DESCOMPOSICION DE VECTORES<br /></strong></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial'><span style='font-size:12pt'><strong> )</strong></span><span style='font-size:10pt'>30º</span><span style='font-size:12pt'><strong><br /> </strong></span></span></p><p><span style='font-family:Arial'><span style='font-size:12pt'><strong><br /> </strong></span><span style='font-size:10pt'>Comp Fx = 35 N<br /></span></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Descomposición de vectores por el método analítico<br /></span></p><ul><li><span style='font-family:Arial; font-size:12pt'>Para calcular la comp. "Fx" se aplica la siguiente formula<br /></span></li></ul><p><span style='font-family:Arial; font-size:12pt'> Fx= Rx cos <<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Fx= (40 N) (cos 30º)<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Fx= (40 N) (0.8660)<br /></span></p><p style='margin-left: 36pt'> <br /> </p><p><span style='font-family:Arial; font-size:12pt'> Fx= <br /></span></p><p style='text-align: center'><br /> </p><ul><li><div><span style='font-family:Arial; font-size:12pt'>Para calcular la comp. "Fy" se aplica la siguiente formula por el método grafico.<br /></span></div><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>Fy= Rx sen <<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>Fy = ( 40 N) (sen 30º)<br /></span></p></li></ul><p><span style='font-family:Arial; font-size:12pt'> Fy=(40N) (0.5)<br /></span></p><p style='margin-left: 36pt'> <br /> </p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'> Fy=<br /></span></p><p style='margin-left: 36pt'><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>EJERCICIOS PROPUESTOS<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- un ciclista efectúa dos desplazamientos, el primero de 7 km al norte y el segundo de 5 km al este.<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Calcular.<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>a).-¿Cuál es la distancia total recorrida por el ciclista? <span style='color:red'>dt= 7 km + 5km = 12 km</span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'>b).-Encuentre gráficamente cual es su desplazamiento resultante, así como la dirección en que actúa y el valor del ángulo medido respecto al este. <span style='color:red'>Desplazamiento = 8.6 km R= 8.6 km con un Angulo. 54º<br /></span></span></p><p><span style='font-family:Arial'><span style='font-size:12pt'><br /> <table border='0' style='border-collapse:collapse'><colgroup><col style='width:29px'/><col style='width:31px'/><col style='width:28px'/><col style='width:33px'/><col style='width:29px'/><col style='width:31px'/><col style='width:33px'/><col style='width:28px'/><col style='width:28px'/><col style='width:33px'/><col style='width:28px'/><col style='width:28px'/><col style='width:34px'/><col style='width:31px'/><col style='width:28px'/><col style='width:33px'/><col style='width:26px'/><col style='width:25px'/><col style='width:28px'/><col style='width:31px'/></colgroup><tbody valign='top'><tr style='height: 42px'><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'><p> </p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p> </p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'><p> </p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td></tr><tr style='height: 38px'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td></tr><tr style='height: 42px'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; 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border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p> </p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td></tr></tbody></table></span><p style='text-align: center'><br /> </p><p><span style='font-size:12pt'>2.- un jugador de futbol americano efectúa los siguientes desplazamientos: 6 m al este, 4m en dirección noreste y finalmente 2 m al norte .</span><span style='color:red; font-size:10pt'>dt=6m+4m+2 m<br /></span></p><p><span style='font-size:10pt'><span style='color:black'>a).-¿Cuál es la distancia total que recorre? </span><span style='color:red'>dt= 12m<br /></span></span></p><p><span style='font-size:10pt'><span style='color:black'>b) Encuentra en forma grafica cual fue su desplazamiento resultante, en que dirección actúa y cual es el valor del ángulo medido respecto al este. </span><span style='color:red'>R= 10.1 m con un angulo de 29º</span><span style='color:black'><br /> </span></span></p><p style='text-align: center'><br /> <img alt='' src='http://www.sc.ehu.es/sbweb/fisica/cinematica/rectilineo/Cine_01.gif' align='left'/>MOVIMIENTO RECTILINEO UNIFORME (MRU)<br /><br /><br />Un movimiento es rectilíneo cuando el móvil describe una trayectoria recta y es uniforme cuando su velocidad es constante en el tiempo dado que su aceleración es nula. Nos referimos a el mediante el acrónico MRU.<br />Es cuando un movimiento sigue una trayectoria recta en la cual realiza desplazamientos iguales en tiempo constante.<br /><br />TIEMPODISTANCIAEn 1 seg.2 metrosEn 2 seg.4 metrosEn 3 seg.6 metros<br />En cada incremento de 1 segundo tiene un incremento de 2 metros en su desplazamiento.<br /><br />EL MRU SE CARACTERIZA POR:<br />La velocidad se representa por medio de la siguiente formula.<br /> </p><p style='background: white'><span style='color:black; font-size:12pt'> V= <span style='text-decoration:underline'> d </span>=<span style='text-decoration:underline'> d2-d1 <br /></span></span></p><p style='background: white'><span style='color:black; font-size:12pt'> T t2-t1<br /></span></p><p style='background: white'><br /> </p><p style='background: white'><span style='color:black; font-size:12pt'> d= Vx para calcular la distancia<br /></span></p><p style='background: white'> <br /> </p><p style='background: white'><span style='color:black; font-size:12pt'> t= <span style='text-decoration:underline'>d </span><br /> </span></p><p style='background: white'><span style='color:black; font-size:12pt'> v para calcular el tiempo<br /></span></p><p style='background: white'><br /> </p><ul><li><div style='background: white'><span style='color:black; font-size:12pt'>la relación de distancia sobre tiempo la velocidad es constante.<br /></span></div></li></ul></span></p><p style='text-align: center; background: white; margin-left: 25pt'><br /> </p><p style='text-align: center; background: white; margin-left: 25pt'><span style='color:black; font-family:Arial; font-size:12pt'><strong>Datos de movimiento de un cuerpo<br /></strong></span></p><p style='text-align: center; background: white; margin-left: 25pt'><br /> </p><div style='margin-left: 25pt'><table border='0' style='border-collapse:collapse'><colgroup><col style='width:84px'/><col style='width:60px'/><col style='width:62px'/><col style='width:60px'/><col style='width:62px'/><col style='width:60px'/><col style='width:62px'/><col style='width:67px'/></colgroup><tbody valign='top'><tr style='height: 74px; background: #e36c0a'><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>Numero de intervalo</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>Ti<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(s)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>D1<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(m)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>T2<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(s)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>D2<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(m)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>t<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(s)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>D<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(m)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>d/t<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'> (m/s)</span></p></td></tr><tr style='height: 24px; background: #ffc000'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>0</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>0</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 24px; background: #e36c0a'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 25px; background: #ffc000'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>3</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>3</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>6</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 24px; background: #e36c0a'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>3</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>6</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>8</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 25px; background: #ffc000'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>5</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>8</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>5</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>10</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 25px; background: #e36c0a'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>6</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>5</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>10</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>6</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>12</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr></tbody></table></div><p style='text-align: center; background: white; margin-left: 25pt'><br /> </p><p style='text-align: center; background: white; margin-left: 25pt'><br /> </p><p style='background: white'><br /> </p><p style='background: white'><span style='color:black; font-family:Arial; font-size:12pt'> Para conocer la velocidad en el MRU se aplica la función tangente.<br /></span></p><p style='text-align: center; background: white'><span style='color:black; font-family:Arial; font-size:12pt'>Tan= <span style='text-decoration:underline'>Cat. Op<br /></span></span></p><p style='text-align: center; background: white'><span style='color:black; font-family:Arial; font-size:12pt'> Cat. ady.<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>Tan= <span style='text-decoration:underline'>8 m </span>= 2 m/s<span style='text-decoration:underline'><br /> </span></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>4 s<br /></span></p><p style='text-align: center'><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Conclusión: En el MRU la función tangente tiene el mismo valor de la formula de la velocidad resultante.<br /></span></p><p><br /> </p><ul><li><span style='font-family:Arial; font-size:12pt'>Al graficar los datos se obtiene una línea recta. Esta línea representa la velocidad e indica que esta permanece constante.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La pendiente de la grafica distancia-tiempo es la resultante entre las dos variables, por lo tanto la velocidad es una magnitud vectorial.<br /></span></li></ul><p><br /> </p><p><br /> </p><p style='text-align: center'><span style='font-size:18pt'><strong>Aceleración y movimiento rectilíneo uniforme variado <br /></strong></span></p><p style='text-align: center'><span style='font-size:18pt'><strong><br /> </strong></span></p><p><br /> </p><p><strong>ACELERACIÓN.<br /></strong></p><ul><li>Es la variación de la velocidad de un móvil en cada unidad de tiempo.<br /></li><li>Se expresa con la fórmula:<br /></li></ul><p><span style='font-size:18pt'><strong><br /> </strong></span></p><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p><br /> </p><ul><li>Si el móvil no parte del reposo, la aceleración es igual a:<br /></li></ul><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><strong><br /> </strong></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><ul><li>Para calcular la V<sub>f</sub> al cabo de cierto tiempo, se calcula mediante la ecuación:<br /></li></ul><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><ul><li><div><span style='font-family:Arial; font-size:12pt'><strong>La aceleración será positiva cuando:<br /></strong></span></div><p><span style='font-family:Arial; font-size:12pt'>*La velocidad es de signo positivo y experimenta un aumento<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>*la velocidad es de signo negativo y sufre una disminución, es decir, un frenado.<br /></span></p></li><li><div><span style='font-family:Arial; font-size:12pt'>La aceleración es negativa cuando:<br /></span></div><p><span style='font-family:Arial; font-size:12pt'>*la velocidad es de signo negativo y tiene un aumento<br /></span></p><p><br /> </p></li></ul><p><br /> </p><p><span style='color:#00b050; font-family:Arial; font-size:14pt'><strong>Ejercicios propuestos del M. R. U. V <br /></strong></span></p><p><span style='font-family:Arial; font-size:12pt'>Un automóvil adquiere una velocidad de 40 km/h al sur en 4 s ¿cual es su aceleración en m/s? <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Datos: formulas conversión sustitución <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>v= 40 km/h a = <span style='text-decoration:underline'>v <br /></span></span></p><p><span style='font-family:Arial; font-size:12pt'>t= 4 s t 1 <span style='text-decoration:underline'>km</span>= <span style='text-decoration:underline'>1000 m </span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'>a= h 3600s<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> 40 <span style='text-decoration:underline'>km </span> = x a= <span style='text-decoration:underline'>11.11 m/s<br /></span></span></p><p><span style='font-family:Arial; font-size:12pt'> h 4 s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> X = (<span style='text-decoration:underline'>40 km</span>) (<span style='text-decoration:underline'>1000m)<br /></span></span></p><p><span style='font-family:Arial; font-size:12pt'> h 3600s a = 2.77 m/s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> 1 <span style='text-decoration:underline'>km</span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'> h<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> x = 11.111 m/s <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Determina la rapidez que llevará un ciclista a los 5 s, si al bajar por una pendiente adquiere una aceleración de 1.5 m/s y parte con una rapidez inicial de 3 m/s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Datos: formula sustitución <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> t: 5 s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> a: 1.5 m/s vf= vo + at vf= 3 m/s + 1.5 m/s (5 s)<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Vo: 3 m/s vf= 3m/s + 7.5 m/s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Vf: vf= 10.5 m/s <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Un móvil tiene una velocidad inicial de 4m/s al sur y experimenta una aceleración de 2 m/s la cual dura 12 s. calcular:<br /></span></p><ol><li><span style='font-family:Arial; font-size:12pt'>que desplazamiento tiene a los 12 s<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>que velocidad lleva a los 12 s <br /></span></li></ol><p><span style='font-family:Arial; font-size:12pt'>Datos: formulas: sustitución <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Vo: 4 m/s al sur d: (4m/s x 12s) + (2m/s) (12s)<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> a: 2 m/s d: vo t + at <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> t: 12 s 2<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> d: d: 48 m + 144 m <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> vf: vf: vo + at d: 192 m al sur<br /></span></p><p><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>vf: 4 m/s + (2m/s x 12s)<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> vf: 4m/s +24 m <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> VF: 28 m/s al sur <br /></span></p><p><span style='color:blue; font-family:Arial; font-size:14pt'><strong>Aceleración media <br /></strong></span></p><p><span style='font-family:Arial; font-size:12pt'>Cuando un móvil varía su velocidad es necesario determinar su aceleración media aplicando la siguiente formula.<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'> am: vf- vo<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> tf- to<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Ecuaciones para calcular desplazamiento<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- d: vot + <span style='text-decoration:underline'>at</span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'> 2<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>2.- vf – vo<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> 2 a <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>3.- d: vf + vo t <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> 2 <br /></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Cuando la velocidad inicial vale cero las tres ecuaciones anteriores se reducen a las siguientes:<br /></span></p><p><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>1. - d. - at<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>2<br /></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>2. - d. vf<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'> 2 a <br /></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>3. - d: vf<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>2 t<br /></span></p><p style='text-align: center'><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Ecuaciones para calcular velocidades finales:<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- vf: vo + at <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>2.- vf: vO + 2 at <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Si la velocidad es cero las ecuaciones anteriores se reducen a las siguientes expresiones.<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- vf: at<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>2.- vf: 2 ad <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Ejercicios:<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- determina la velocidad media de un móvil que lleva una velocidad inicial de 3 m/s y su velocidad final es de 4.2 m/s<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Datos: formula sustitución <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Vo: 3m/s vm: <span style='text-decoration:underline'>3m/s + 4.2 m/s</span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'>Vf: 4.2 m/s vm: <span style='text-decoration:underline'>vo + vf</span> 2 <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Vm:? 2 Vm: 3.6 m/s <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>2.- calcular el tiempo en horas en que un automóvil recorre una distancia de 3 km si lleva una velocidad media de 50 km/h al sur<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Datos: formulas sustitucion <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> d: 3 km<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>vm: 50 km/h t: d t: 3 km<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> t: vm 50 km/h<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'> Vm: d t: 0.06 h <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> t<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><br /> </span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:14pt'><strong>CAIDA LIBRE<br /></strong></span></p><p style='text-align: center'><br /> </p><p><span style='font-family:Arial; font-size:14pt'><strong>Definición<br /></strong></span></p><p><br /> </p><ul><li><span style='font-family:Arial; font-size:12pt'>Se define como la caída de un cuerpo sobre la superficie de la tierra sin ninguna resistencia originada por el aire.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Todos los cuerpos ya sean grandes o pequeños, en ausencia de fricción caen a la tierra con la misma aceleración<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La aceleración gravitacional produce sobre los cuerpos con caída libre un movimiento uniforme variado.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>En caída libre la velocidad aumenta en forma constante y la aceleración permanece fija <br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La aceleración de la tierra es de 9.8 m/s<sup>2. </sup>Es una magnitud vectorial cuya dirección esta dirigida hacia el centro de la tierra, por lo que su valor debe ser negativo.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La aceleración de la tierra se representa con la letra "g"<br /></span></li><li><div><span style='font-family:Arial; font-size:12pt'>Para resolver problemas de caída libre se utilizan las mismas ecuaciones de MRUV, pero se cambia la letra a de aceleración por g que representa la aceleración de la gravedad y la letra "d" de distancia por "h" que representa la altura<br /></span></div><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p></li></ul><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:14pt'><strong>TIRO VERTICAL<br /></strong></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p><br /> </p><p style='margin-left: 25pt'><span style='font-family:Arial; font-size:12pt'><strong>TIRO VERTICAL<br /></strong></span></p><p style='margin-left: 25pt'><br /> </p><ul><li><span style='font-family:Arial; font-size:12pt'>Es el movimiento de un cuerpo que se lanza verticalmente hacia arriba observándose que su velocidad va disminuyendo hasta anularse cuando alcanza su máxima altura.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>El tiempo empleado en subir, es el mismo utilizado en bajar<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>El tiro vertical sigue las mismas leyes de la caída libre de los cuerpos, por tanto, emplea las mismas ecuaciones<br /></span></li><li><div><span style='font-family:Arial; font-size:12pt'>Para calcular la altura máxima que alcanza un cuerpo, se utiliza las siguientes ecuaciones:<br /></span></div><p> <br /> </p></li></ul><p style='text-align: center'><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><ul><li><div><span style='font-family:Arial; font-size:12pt'>Para calcular el tiempo que tarda en subir utilizamos la ecuación:<br /></span></div><p><br /> </p></li></ul><p><br /> </p><p> <br /> </p><p><br /> </p><p style='margin-left: 25pt'><br /> </p><ul><li><div><span style='font-family:Arial; font-size:12pt'>Como el tiempo que tarda en subir es el mismo para bajar entonces el tiempo de permanencia en el aire será:<br /></span></div><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>EJERCICIOS PROPUESTOS DE TIRO VERTICAL</span><br /> </p></li></ul><p><span style='color:#000045; font-family:Arial; font-size:12pt'>Se lanza un cuerpo verticalmente hacia arriba con una velocidad inicial de 100 m/s, luego de 4 s de efectuado el lanzamiento su velocidad es de 60 m/s.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>a) ¿Cuál es la altura máxima alcanzada?.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>b) ¿En qué tiempo recorre el móvil esa distancia?.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>c) ¿Cuánto tarda en volver al punto de partida desde que se lo lanzo?.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>d) ¿Cuánto tarda en alcanzar alturas de 300 m y 600 m?.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>Usar g = 10 m/s ².<br /></span></p><p style='margin-left: 2pt'><br /> </p><p style='margin-left: 2pt'><span style='color:#000033; font-family:Arial; font-size:12pt; text-decoration:underline'><strong>DESARROLLO<br /></strong></span></p><p style='margin-left: 6pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><em>Datos</em>:<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>v<sub>0</sub> = 100 m/s<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>v<sub>f</sub> = 60 m/s<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>t = 4 s<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>y<sub>1</sub> = 300 m<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>y<sub>2</sub> = 600 m<br /></span></p><p style='margin-left: 36pt'><br /> </p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt; text-decoration:underline'><strong>FORMULAS<br /></strong></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>A ) v<sub>f</sub> = v<sub>0</sub> + g.t<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>B) y = v<sub>0</sub>.t + g.t ²/2<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>C) v<sub>f</sub> ² - v<sub>0</sub> ² = 2.g.h<br /></span></p><p style='margin-left: 3pt'> <br /> </p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt; text-decoration:underline'><strong>SUSTITUCION<br /></strong></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'> a) Para la altura máxima v<sub>f</sub> = 0, de la ecuación (3):<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>-v<sub>0</sub> ² = 2.g.h<br/>h<sub> máx</sub> = -v<sub>f</sub> ²/(2.g)Þ h<sub> máx</sub> = -(100 m/s) ²/[2.(-10 m/s ²)]<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>h<sub> máx</sub> = 500 m<br /></strong></span></p><p style='margin-left: 3pt'><br /> </p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>b) De la ecuación (1) y para v<sub>f</sub> = 0:<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>t = v<sub>0</sub>/g<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>t = (-100 m/s)/(-10 m/s ²)<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>t = 10 s<br /></strong></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>c) Recordemos que en tiro vertical, cuando un objeto es lanzado hacia arriba y luego cae, cuando vuelve a pasar por el punto de partida posee la misma velocidad que en el momento del lanzamiento <strong>pero con sentido contrario</strong> (v<sub>f</sub> = -v<sub>0</sub>).<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>Podemos asegurar que el resultado pedido es el doble del tiempo que requirió para alcanzar la altura máxima.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>t = 20 s</strong><br /> </span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>e) No puede alcanzar una altura de 600 m porque la máxima es de 500 m. Para h = 300 m empleamos la ecuación (2):<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>0 = v<sub>0</sub>.t + g.t ²/2 - y<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>Aplicamos la ecuación cuadrática que dará dos resultados: <br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>t<sub>1</sub> = 3,68 s</strong><br /> </span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>t<sub>2</sub> = 16,32 s</strong><br /> </span></p><p style='margin-left: 3pt'><br /> </p><p style='text-align: center'><span style='font-family:Arial Narrow; font-size:18pt'><strong>Tiro parabólico oblicuo<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Tiro parabólico oblicuo. Se caracteriza por la trayectoria que sigue un cuerpo cuando es lanzado con una velocidad inicial que forma un ángulo con el eje horizontal.<br /></span></p><p style='text-align: center; margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'>1.- Un jugador le pega a una pelota con un ángulo de 37° con respecto al plano horizontal, comunicándole una velocidad inicial de 15 m/seg. Calcular a) e tiempo que dura en el aire, b) La altura máxima alcanzada, c) El alcance horizontal de la pelota.<br /></span></p><p style='margin-left: 18pt'><br /> </p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Datos Fórmulas Sustitución<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Vo = 15 m/seg Vov = Vo sen θ Vov = 15 m/seg x sen 37°<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>θ= 37° VH = Vo cos θ Vov = 15 m/seg x 0.6018<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>g = -9.8 m/seg2. t (aire) = - 2Vov/g Vov = 9.027 m/seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>t (aire) = ? h max = - V2ov/2g VH = 15 m/se x cos 37°<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>h max= ? dH = VH t (aire) VH = 15 m/seg x 0.7986<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>dH= ? VH = 11.979 m/seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> t aire= - <span style='text-decoration:underline'>2 (9.027 m/seg)</span><strong><br /> </strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><strong> </strong>-9.8 m/seg2.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> <strong>t aire = 1.842 seg<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><strong> </strong>h max = - <span style='text-decoration:underline'>(9.027 m/seg)2 =</span><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> 2 (- 9.8 m/seg2.)<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> <strong>h max = 4.157 metros<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><strong> </strong>dH = 11.979 m/seg x 1.842 seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> <strong>dH = 22.06 metros<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>2.- Un proyectil se lanza con una velocidad inicial de 200 m/seg si se desea que dé en un blanco localizado a 2500 metros, calcular: a) El ángulo con el cual debe ser lanzado b) el tiempo que tarda en llegar al blanco (tiempo en el aire).<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Datos Fórmulas Sustitución<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Vo = 200 m/seg - sen 2 θ= <span style='text-decoration:underline'>dHg</span> - sen 2 θ= <span style='text-decoration:underline'>2500 m x(- 9.8 m/seg2)</span>.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>dH = 2500 m Vo2. (200 m/seg)2.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>g = -9.8 m/seg2. Vov = Vo sen θ sen 2 θ = 0.6127<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>a) θ= t (aire)= -<span style='text-decoration:underline'>2Vov </span> 2 θ = ángulo cuyo seno es g 0.6127 <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>b) t aire =? 2 θ= 37.76°<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> <strong>θ= 18.88°<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><strong> Vov = </strong>200 m/seg x sen 18.88°<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> Vov = 200 m/seg x 0.3230= 64.6 m/seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> t (aire) = - <span style='text-decoration:underline'>2 x 64.6 m/seg = </span><strong>13.18 seg</strong><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> - 9.8 m/seg2.<br /></span></p><ul><li><span style='font-family:Arial; font-size:12pt'>3.- ¿Cuál será la velocidad inicial con que se batea una pelota de beisbol, si es golpeada con un ángulo de 40° respecto a la horizontal, si la altura máxima que alcanza es de 10.2 metros y su desplazamiento horizontal es de 48.62 metros?<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Datos Fórmula<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Vo = ? dH = -<span style='text-decoration:underline'> Vo2 sen 2 θ <br /></span></span></li><li><span style='font-family:Arial; font-size:12pt'>Θ = 40° g<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>h max = 10.2 m despejando Vo tenemos:<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>dH = 48.62 m Vo = √<span style='text-decoration:underline'>dHg<br /></span></span></li><li><span style='font-family:Arial; font-size:12pt'>g = -9.8 m/seg2. sen 2 θ<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Sustitución y resultado:<br /></span></li><li><div><span style='font-family:Arial; font-size:12pt'>Vo = √ <span style='text-decoration:underline'>48.62 m x -9.8 m/seg2. </span> = √<span style='text-decoration:underline'> 476.476 m2/s2.<br /></span></span></div><ul style='margin-left: 108pt'><li><span style='font-family:Arial; font-size:12pt'>sen (80°) 0.9848<br /></span></li></ul></li><li><span style='font-family:Arial; font-size:12pt'>Vo = <strong>22 m/seg</strong>.<br /></span></li></ul><p><br /> </p><p><br /> </p><p><br /> </p><p style='text-align: center; margin-left: 3pt'><span style='font-family:Arial; font-size:12pt'><strong>TIRO PARABOLICO<br /></strong></span></p><p style='margin-left: 3pt'><br /> </p><p><span style='font-size:12pt'>Se denomina <strong>tiro parabólico</strong> al realizado por un objeto cuya trayectoria describe una <a title='Parábola (matemática)' href='http://es.wikipedia.org/wiki/Par%C3%A1bola_(matem%C3%A1tica)'>parábola</a>. Se corresponde con la trayectoria ideal de un <a title='Proyectil' href='http://es.wikipedia.org/wiki/Proyectil'>proyectil</a> que se mueve en un medio que no ofrece resistencia al avance y que está sujeto a un <a title='Campo gravitatorio' href='http://es.wikipedia.org/wiki/Campo_gravitatorio'>campo gravitatorio</a> uniforme.<br /></span></p><p><span style='font-size:12pt'>Puede ser analizado como la composición de dos movimientos rectilíneos: un <a title='Movimiento rectilíneo uniforme' href='http://es.wikipedia.org/wiki/Movimiento_rectil%C3%ADneo_uniforme'>movimiento rectilíneo uniforme</a> horizontal y un <a title='Movimiento rectilíneo uniformemente acelerado' href='http://es.wikipedia.org/wiki/Movimiento_rectil%C3%ADneo_uniformemente_acelerado'>movimiento rectilíneo uniformemente acelerado</a> vertical.<br /></span></p><div><table border='0' style='border-collapse:collapse'><colgroup><col style='width:54px'/></colgroup><tbody valign='top'><tr><td style='padding-top: 1px; padding-left: 1px; padding-bottom: 1px; padding-right: 1px' vAlign='middle'><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'><br /> </span> </p></td></tr></tbody></table></div><h2><span style='font-family:Arial; font-size:12pt'>Tipos de movimiento parabólico <br /></span></h2><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><br /> </span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Movimiento de media parábola<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>El movimiento de media parábola o semiparabólico (lanzamiento horizontal) <br /></span></p><ul><li><span style='font-family:Arial; font-size:12pt'>Se puede considerar como la composición de un avance horizontal rectilíneo uniforme y la <a title='Caída libre' href='http://es.wikipedia.org/wiki/Ca%C3%ADda_libre'>caída libre</a>. <br /></span></li></ul><p><span style='font-family:Arial; font-size:12pt'>El movimiento parabólico completo <br /></span></p><ul><li><span style='font-family:Arial; font-size:12pt'>Se puede considerar como la composición de un avance horizontal rectilíneo uniforme y un lanzamiento vertical hacia arriba, que es un movimiento rectilíneo uniformemente acelerado hacia abajo (MRUA) por la acción de la <a title='Gravedad' href='http://es.wikipedia.org/wiki/Gravedad'>gravedad</a>. <br /></span></li></ul><p><span style='font-size:12pt'>En condiciones ideales de resistencia al avance nulo y campo gravitatorio uniforme, lo anterior implica que:<br /></span></p><ol><li><span style='font-family:Arial; font-size:12pt'>Un cuerpo que se deja caer libremente y otro que es lanzado horizontalmente desde la misma <a title='Alto dimensional' href='http://es.wikipedia.org/wiki/Alto_dimensional'>altura</a> tardan lo mismo en llegar al suelo. <br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La independencia de la <a title='Masa' href='http://es.wikipedia.org/wiki/Masa'>masa</a> en la caída libre y el lanzamiento vertical es igual de válida en los movimientos parabólicos. <br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Un cuerpo lanzado verticalmente hacia arriba y otro parabólicamente completo que alcance la misma altura tarda lo mismo en caer. <br /></span></li></ol><h2><span style='font-family:Arial; font-size:12pt'>Ecuaciones del tiro parabólico <br /></span></h2><p><br /> </p><p><span style='font-size:12pt'>Hay dos ecuaciones que rigen el tiro parabólico:<br /></span></p><ol><li><span style='font-family:Arial; font-size:12pt'><br /> </span></li><li><span style='font-family:Arial; font-size:12pt'><br /> </span></li></ol><p><span style='font-size:12pt'>Donde:<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>es el módulo de la velocidad inicial. <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>es el ángulo de la velocidad inicial sobre la horizontal. <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>es la aceleración de la gravedad. <br /></span></p><p><span style='font-size:12pt'>La velocidad inicial se compone de dos partes:<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>que se denomina componente horizontal de la velocidad inicial. <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>En lo sucesivo <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>que se denomina componente vertical de la velocidad inicial. <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>En lo sucesivo <br /></span></p><p><span style='font-size:12pt'>Se puede expresar la velocidad inicial de este modo:<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'> : [ecu. 1] <br /></span></p><p><span style='font-size:12pt'>Será la que se utilice, excepto en los casos en los que deba tenerse en cuenta el ángulo de la velocidad inicial.<br /></span></p><p><br /> </p><p><br /> </p><p style='text-align: center'><span style='font-size:16pt'><strong>Tiro horizontal<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>Tiro parabólico horizontal. Se caracteriza por la trayectoria o camino curvo que sigue un cuerpo al ser lanzado horizontalmente al vacío, resultado de dos movimientos independientes: un movimiento horizontal con velocidad constante y otro vertical, el cual se inicia con una velocidad cero y va aumentando en la misma proporción de otro cuerpo que se dejará caer del mismo punto en el mismo instante. <br /></span></p><p><span style='font-family:Arial Narrow; font-size:14pt'> EJERCICIOS PROPUESTOS<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>1- Se lanza una piedra horizontalmente con una velocidad de 25 m/seg desde una altura de 60 metros. Calcular: a) el tiempo que tarda en llegar al suelo, b) la velocidad vertical que lleva a los 2 segundos, c) La distancia horizontal a la que cae la piedra.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>Datos Fórmulas Sustitución<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> ____ _________________<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>VH = 25 m/seg a) t caer = √2h/g t caer = √2 (-60 m)/-9.8 m/seg2.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>h = -60 metros b) V2 seg= g t <strong>t caer = 3.5 seg</strong><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>g= - 9.8 m/seg2. <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> V2seg = -9.8 m/seg2x 2 seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>a) t caer =? c) dH= VH t <strong>V2 seg= - 19.6 m/seg</strong><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>b) V2 seg= ? dH= 25 m/seg x 3.5 seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>c) dH= ? <strong>dH = 87.5 metros </strong><br /> </span></p><p><br /> </p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>2.- Una pelota es lanzada horizontalmente desde una ventana con una velocidad inicial de 10 m/seg y cae al suelo después de 5 segundos: Calcular a) ¿ A qué altura se encuentra la ventana? b) ¿A qué distancia cae la pelota?<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>Datos Fórmulas Sustitución<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>VH = 10 m/seg a) h = gt2/2 a) h =<span style='text-decoration:underline'> -9.8 m/seg2x (5 seg)2<br /></span></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>t caer = 5 seg 2 <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> b) dH = VHtcaer <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>g = -9.8 m/seg2. a) <strong>h = -122.5 metros</strong><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>a) h = ? b) dH = 10 m/seg x 5 seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>b) dH =? b) <strong>dH = 50 metros</strong><br /> </span></p><p><br /> </p><p><span style='font-family:Arial Narrow; font-size:14pt'>3.- Un avión vuela horizontalmente con una velocidad de 800 km/h y deja caer un proyectil desde una altura de 500 m respecto al suelo. Calcular: a) ¿Cuánto tiempo transcurre antes de que el proyectil se impacte en el suelo? b) ¿Qué distancia horizontal recorre el proyectil después de iniciar su caída?<br /></span></p><p><span style='font-family:Arial Narrow; font-size:14pt'> Datos Fórmulas <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>VH = 800 km/h a) t (caer) = √2h/g <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>h = -500 m b) dH = VH t (caer.)<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>g = -9.8 m/seg2. Sustitución y resultados.<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>a) t(caer)=? a) t (caer) = √2 (-500 m)/ -9.8 m/seg2. <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> b) dH = ? a) t( caer) = 10.10 seg.<br /></span></p><p><br /> </p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>Conversión de km/h a m/seg:<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>800 <span style='text-decoration:underline'>km</span> x <span style='text-decoration:underline'>1000 m</span> x <span style='text-decoration:underline'> 1 h </span>= 222.22 m/seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> h 1 km 3600 seg<br /></span></p><p> <br /> </p><ol><li><span style='font-family:Arial Narrow; font-size:14pt'>dH = 222.22 m/seg x 10.10 seg = 2244.42 m<br /></span></li></ol><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:#993300'><strong><em>IMPORTANCIA DEL ESTUDIO DE LA CINEMATICA.</em><br /> </strong></span></p><ul><li><span style='color:#3366ff'>Permite conocer y predecir en qué lugar se encontrará un cuerpo, qué velocidad <br /></span></li><li><span style='color:#3366ff'>tendrá al cabo de cierto tiempo o en lapso llegará a su destino.<br /></span></li><li><span style='color:#3366ff'>Permite hacer la descripción del movimiento de un cuerpo.<br /></span></li><li><span style='color:#3366ff'>Permite precisar a cada instante, la posición de una partícula en el espacio.<br /></span></li></ul><p><br /> </p><p><span style='color:#ff6600'><strong><em>CONCEPTO DE PARTICULA MATERIAL EN MOVIMIENTO<br /></em></strong></span></p><p><span style='color:#99cc00'><strong>Movimiento.-</strong> Es la variación de la posición de una partícula respecto a un punto considerado fijo.<br /></span></p><p><span style='color:#99cc00'><strong>Partícula Material en Movimiento.- Es cualquier objeto material o cuerpo físico en movimiento.<br /></strong></span></p><p><strong>Ejemplo:<br /></strong></p><p> <br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:#99cc00'><strong>La trayectoria<br /></strong></span></p><p><span style='color:#99cc00'><strong>de una partícula <br /></strong></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:red'><strong><em>SISTEMAS DE REFERENCIAS.</em><br /> </strong></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:#99cc00'><strong>Para describir la posición de una partícula se utiliza un sistema de coordinadas.<br /></strong></span></p><ul><li>El eje se corta perpendicularmente en un punto 0 llamado origen.<br /></li><li>El eje horizontal es el eje de las abscisas o de las <em>x</em><br /> </li><li>El eje vertical es el eje de las ordenadas o de las <em>y</em><br /> </li></ul><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial Narrow'>La posición de M está determinada por dos magnitudes:<br /></span></p><p style='margin-left: 70pt'><span style='font-family:Arial Narrow'>La abscisa 0 Q y la Ordenada 0 P<br /></span></p><p><span style='font-family:Arial Narrow'>La posición de de la partícula es:<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'>M = (x, y)<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'>Donde: x = 40<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'> y = 30<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'>Por lo tanto:<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'> M = (40, 30)<br /></span></p><p><span style='font-family:Arial Narrow'>La posición de M también puede representarse por el vector es llamado <strong>vector de <br /></strong></span></p><p><span style='font-family:Arial Narrow'><strong> Posición, </strong>cuyos componentes rectangulares son<strong> x, y.<br /></strong></span></p><p><span style='font-family:Arial Narrow'><strong>Según el cuadrante en que se encuentren las coordenadas, éstas tendrán signo positivo o negativo, según la posición de la partícula.<br /></strong></span></p><p><strong><br /> </strong></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:#999999'><strong><em>DISTANCIA, DESPLAZAMIENTO, VELOCIDAD Y RAPIDEZ.<br /></em></strong></span></p><p><strong>Distancia:<br /></strong></p><ul><li>Es la longitud que recorre un móvil sin importar la dirección del recorrido.<br /></li><li>Es una magnitud escalar.<br /></li></ul><p><br /> </p><ul><li><strong>Desplazamiento<br /></strong></li><li>Es la distancia medida en una dirección particular entre dos puntos: el de partida y el de llegada.<br /></li><li>Es una magnitud vectorial.<br /></li></ul><p><br /> </p><ul><li><strong>Rapidez.<br /></strong></li><li>Es una magnitud escalar que relaciona la distancia recorrida con el tiempo. velocidad.<br /></li><li><br /> </li></ul><p><br /> </p><ul><li><strong>Velocidad.</strong><br /> </li><li>Es una magnitud vectorial.<br /></li><li>Es la rapidez con que se mueve un cuerpo.<br /></li><li>Es una magnitud vectorial que relaciona el cambio de posición (o desplazamiento) con el tiempo. <br /></li></ul><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:purple; font-family:Arial; font-size:14pt'><br /> </span> </p></span>Karlahttp://www.blogger.com/profile/05031254835401085216noreply@blogger.com0tag:blogger.com,1999:blog-8633242566433811702.post-89612983362503034532009-11-12T20:16:00.001-08:002009-11-12T20:16:03.575-08:00<span xmlns=''><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><div><table border='0' style='border-collapse:collapse'><colgroup><col style='width:192px'/><col style='width:192px'/><col style='width:192px'/></colgroup><tbody valign='top'><tr style='background: yellow'><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:18pt'><strong>Magnitud</strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='font-family:Arial; font-size:18pt'><strong>Nombre<br /></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='font-family:Arial; font-size:18pt'><strong>Símbolo</strong></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Superficie</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro cuadrado</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m2<br /></span></p></td></tr><tr style='background: #92d050'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Volumen</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro cúbico</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m3<br /></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Velocidad</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro por segundo</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m/s<br /></span></p></td></tr><tr style='background: #92d050'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Aceleración</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro por segundo cuadrado</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m/s2<br /></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Número de ondas</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>metro a la potencia menos uno</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m-1</span></p></td></tr><tr style='background: #92d050'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Masa en volumen</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>kilogramo por metro cúbico</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>kg/m3<br /></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Velocidad angular</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>radián por segundo</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>rad/s<br /></span></p></td></tr><tr style='height: 38px'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:18pt'><strong>MAGNITUD</strong></span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:18pt'><strong>SI</strong></span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:18pt'><strong>CGS</strong></span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:18pt'><strong>INGLES</strong></span></p></td></tr><tr style='height: 22px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Longitud</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Metro (m)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Centímetro(m)<br /></span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie</span></p></td></tr><tr style='height: 22px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Masa</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Kilogramo (kg)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Gramo (g)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Libra</span></p></td></tr><tr style='height: 32px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Tiempo</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Segundo (s)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Segundo (s)</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Segundo (s)</span></p></td></tr><tr style='height: 27px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Área</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Cm2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie2</span></p></td></tr><tr style='height: 26px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Volumen</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>M3</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Cm3</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie3</span></p></td></tr><tr style='height: 32px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Velocidad</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m/s</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Cm/s</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie/s</span></p></td></tr><tr style='height: 28px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Aceleración </span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>m/s2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Cm/s2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Pie/s2</span></p></td></tr><tr style='height: 27px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Fuerza</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Kgm/s newton</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>gcm/s2=dina </span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Librapie/s2=potencial</span></p></td></tr><tr style='height: 28px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Trabajo</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Nm=joule</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Dina cm=baria</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Poental/pie2</span></p></td></tr><tr style='height: 26px; background: #ff3399'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Energía</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Nm=joule</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Dina cm=baria</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Poental/pie</span></p></td></tr><tr style='height: 15px; background: yellow'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Presión </span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>n/m2=pascal</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>Dina/cm2</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:14pt'>Poental pie</span></p></td></tr><tr style='height: 21px'><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p><span style='color:black; font-family:Arial; font-size:14pt'>potencia</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center; background: #ff3399'><span style='color:black; font-family:Arial; font-size:14pt'>Joule/swatt</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center; background: #ff3399'><span style='color:black; font-family:Arial; font-size:14pt'>Ergio/s</span></p></td><td style='padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt'><p style='text-align: center; background: #ff3399'><span style='color:black; font-family:Arial; font-size:14pt'>Poental pie/s</span></p></td></tr></tbody></table></div><p><br /> </p><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:14pt'>CONVERSIONES<br /></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:14pt'>TIPO DE VECTORES<br /></span></p><p><br /> </p><div><table border='0' style='border-collapse:collapse'><colgroup><col style='width:153px'/><col style='width:213px'/><col style='width:208px'/></colgroup><tbody valign='top'><tr style='height: 47px; background: #d6e3bc'><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><strong>TIPO DE VECTOR</strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><strong>DEFINICIÒN</strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><strong><em>REPRESENTACIÒN</em></strong></span></p></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong> Colineal</strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Son aquellos vectores que están contenidos<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>en una misma línea de acción.<br /></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p style='text-align: center'/></td></tr><tr style='background: #d6e3bc'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p> <br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong><em>Concurrente</em></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Son aquellos vectores cuyas líneas de acción,<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>se cortan en un solo punto.<br /></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'/></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong><em>Coplanar</em></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Son aquellos vectores que están contenidos<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>en un mismo plano.<br /></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'/></td></tr><tr style='background: #d6e3bc'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong><em>Iguales</em></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Son aquellos vectores que tienen la misma<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>intensidad, dirección y sentido</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'/></td></tr><tr style='background: #00b0f0'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong><em>Opuesto</em></strong></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p><span style='font-family:Arial; font-size:12pt'>Se llama vector opuesto (-A) de un vector A<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>cuando tienen el mismo módulo, la misma dirección,<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>pero sentido contrario.<br /></span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><br /> </p><p style='text-align: center'/></td></tr></tbody></table></div><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><strong>DESCOMPOSICION DE VECTORES<br /></strong></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial'><span style='font-size:12pt'><strong> )</strong></span><span style='font-size:10pt'>30º</span><span style='font-size:12pt'><strong><br /> </strong></span></span></p><p><span style='font-family:Arial'><span style='font-size:12pt'><strong><br /> </strong></span><span style='font-size:10pt'>Comp Fx = 35 N<br /></span></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Descomposición de vectores por el método analítico<br /></span></p><ul><li><span style='font-family:Arial; font-size:12pt'>Para calcular la comp. "Fx" se aplica la siguiente formula<br /></span></li></ul><p><span style='font-family:Arial; font-size:12pt'> Fx= Rx cos <<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Fx= (40 N) (cos 30º)<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Fx= (40 N) (0.8660)<br /></span></p><p style='margin-left: 36pt'> <br /> </p><p><span style='font-family:Arial; font-size:12pt'> Fx= <br /></span></p><p style='text-align: center'><br /> </p><ul><li><div><span style='font-family:Arial; font-size:12pt'>Para calcular la comp. "Fy" se aplica la siguiente formula por el método grafico.<br /></span></div><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>Fy= Rx sen <<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>Fy = ( 40 N) (sen 30º)<br /></span></p></li></ul><p><span style='font-family:Arial; font-size:12pt'> Fy=(40N) (0.5)<br /></span></p><p style='margin-left: 36pt'> <br /> </p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'> Fy=<br /></span></p><p style='margin-left: 36pt'><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>EJERCICIOS PROPUESTOS<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- un ciclista efectúa dos desplazamientos, el primero de 7 km al norte y el segundo de 5 km al este.<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Calcular.<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>a).-¿Cuál es la distancia total recorrida por el ciclista? <span style='color:red'>dt= 7 km + 5km = 12 km</span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'>b).-Encuentre gráficamente cual es su desplazamiento resultante, así como la dirección en que actúa y el valor del ángulo medido respecto al este. <span style='color:red'>Desplazamiento = 8.6 km R= 8.6 km con un Angulo. 54º<br /></span></span></p><p><span style='font-family:Arial'><span style='font-size:12pt'><br /> <table border='0' style='border-collapse:collapse'><colgroup><col style='width:29px'/><col style='width:31px'/><col style='width:28px'/><col style='width:33px'/><col style='width:29px'/><col style='width:31px'/><col style='width:33px'/><col style='width:28px'/><col style='width:28px'/><col style='width:33px'/><col style='width:28px'/><col style='width:28px'/><col style='width:34px'/><col style='width:31px'/><col style='width:28px'/><col style='width:33px'/><col style='width:26px'/><col style='width:25px'/><col style='width:28px'/><col style='width:31px'/></colgroup><tbody valign='top'><tr style='height: 42px'><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'><p> </p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p> </p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'><p> </p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td></tr><tr style='height: 38px'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td></tr><tr style='height: 42px'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; 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border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p> </p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid 0.5pt'> </td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'> </td></tr></tbody></table></span><p style='text-align: center'><br /> </p><p><span style='font-size:12pt'>2.- un jugador de futbol americano efectúa los siguientes desplazamientos: 6 m al este, 4m en dirección noreste y finalmente 2 m al norte .</span><span style='color:red; font-size:10pt'>dt=6m+4m+2 m<br /></span></p><p><span style='font-size:10pt'><span style='color:black'>a).-¿Cuál es la distancia total que recorre? </span><span style='color:red'>dt= 12m<br /></span></span></p><p><span style='font-size:10pt'><span style='color:black'>b) Encuentra en forma grafica cual fue su desplazamiento resultante, en que dirección actúa y cual es el valor del ángulo medido respecto al este. </span><span style='color:red'>R= 10.1 m con un angulo de 29º</span><span style='color:black'><br /> </span></span></p><p style='text-align: center'><br /> <img alt='' src='http://www.sc.ehu.es/sbweb/fisica/cinematica/rectilineo/Cine_01.gif' align='left'/>MOVIMIENTO RECTILINEO UNIFORME (MRU)<br /><br /><br />Un movimiento es rectilíneo cuando el móvil describe una trayectoria recta y es uniforme cuando su velocidad es constante en el tiempo dado que su aceleración es nula. Nos referimos a el mediante el acrónico MRU.<br />Es cuando un movimiento sigue una trayectoria recta en la cual realiza desplazamientos iguales en tiempo constante.<br /><br />TIEMPODISTANCIAEn 1 seg.2 metrosEn 2 seg.4 metrosEn 3 seg.6 metros<br />En cada incremento de 1 segundo tiene un incremento de 2 metros en su desplazamiento.<br /><br />EL MRU SE CARACTERIZA POR:<br />La velocidad se representa por medio de la siguiente formula.<br /> </p><p style='background: white'><span style='color:black; font-size:12pt'> V= <span style='text-decoration:underline'> d </span>=<span style='text-decoration:underline'> d2-d1 <br /></span></span></p><p style='background: white'><span style='color:black; font-size:12pt'> T t2-t1<br /></span></p><p style='background: white'><br /> </p><p style='background: white'><span style='color:black; font-size:12pt'> d= Vx para calcular la distancia<br /></span></p><p style='background: white'> <br /> </p><p style='background: white'><span style='color:black; font-size:12pt'> t= <span style='text-decoration:underline'>d </span><br /> </span></p><p style='background: white'><span style='color:black; font-size:12pt'> v para calcular el tiempo<br /></span></p><p style='background: white'><br /> </p><ul><li><div style='background: white'><span style='color:black; font-size:12pt'>la relación de distancia sobre tiempo la velocidad es constante.<br /></span></div></li></ul></span></p><p style='text-align: center; background: white; margin-left: 25pt'><br /> </p><p style='text-align: center; background: white; margin-left: 25pt'><span style='color:black; font-family:Arial; font-size:12pt'><strong>Datos de movimiento de un cuerpo<br /></strong></span></p><p style='text-align: center; background: white; margin-left: 25pt'><br /> </p><div style='margin-left: 25pt'><table border='0' style='border-collapse:collapse'><colgroup><col style='width:84px'/><col style='width:60px'/><col style='width:62px'/><col style='width:60px'/><col style='width:62px'/><col style='width:60px'/><col style='width:62px'/><col style='width:67px'/></colgroup><tbody valign='top'><tr style='height: 74px; background: #e36c0a'><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>Numero de intervalo</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>Ti<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(s)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>D1<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(m)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>T2<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(s)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>D2<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(m)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>t<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(s)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>D<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>(m)</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: solid black 0.5pt; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>d/t<br /></span></p><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'> (m/s)</span></p></td></tr><tr style='height: 24px; background: #ffc000'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>0</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>0</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 24px; background: #e36c0a'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 25px; background: #ffc000'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>3</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>3</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>6</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 24px; background: #e36c0a'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>3</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>6</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>8</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 25px; background: #ffc000'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>5</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>4</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>8</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>5</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>10</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr><tr style='height: 25px; background: #e36c0a'><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: solid black 0.5pt; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>6</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>5</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>10</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>6</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>12</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>1</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td><td style='padding-left: 7px; padding-right: 7px; border-top: none; border-left: none; border-bottom: solid black 0.5pt; border-right: solid black 0.5pt'><p style='text-align: center'><span style='color:black; font-family:Arial; font-size:12pt'>2</span></p></td></tr></tbody></table></div><p style='text-align: center; background: white; margin-left: 25pt'><br /> </p><p style='text-align: center; background: white; margin-left: 25pt'><br /> </p><p style='background: white'><br /> </p><p style='background: white'><span style='color:black; font-family:Arial; font-size:12pt'> Para conocer la velocidad en el MRU se aplica la función tangente.<br /></span></p><p style='text-align: center; background: white'><span style='color:black; font-family:Arial; font-size:12pt'>Tan= <span style='text-decoration:underline'>Cat. Op<br /></span></span></p><p style='text-align: center; background: white'><span style='color:black; font-family:Arial; font-size:12pt'> Cat. ady.<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>Tan= <span style='text-decoration:underline'>8 m </span>= 2 m/s<span style='text-decoration:underline'><br /> </span></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>4 s<br /></span></p><p style='text-align: center'><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Conclusión: En el MRU la función tangente tiene el mismo valor de la formula de la velocidad resultante.<br /></span></p><p><br /> </p><ul><li><span style='font-family:Arial; font-size:12pt'>Al graficar los datos se obtiene una línea recta. Esta línea representa la velocidad e indica que esta permanece constante.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La pendiente de la grafica distancia-tiempo es la resultante entre las dos variables, por lo tanto la velocidad es una magnitud vectorial.<br /></span></li></ul><p><br /> </p><p><br /> </p><p style='text-align: center'><span style='font-size:18pt'><strong>Aceleración y movimiento rectilíneo uniforme variado <br /></strong></span></p><p style='text-align: center'><span style='font-size:18pt'><strong><br /> </strong></span></p><p><br /> </p><p><strong>ACELERACIÓN.<br /></strong></p><ul><li>Es la variación de la velocidad de un móvil en cada unidad de tiempo.<br /></li><li>Se expresa con la fórmula:<br /></li></ul><p><span style='font-size:18pt'><strong><br /> </strong></span></p><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p><br /> </p><ul><li>Si el móvil no parte del reposo, la aceleración es igual a:<br /></li></ul><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><strong><br /> </strong></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><ul><li>Para calcular la V<sub>f</sub> al cabo de cierto tiempo, se calcula mediante la ecuación:<br /></li></ul><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><ul><li><div><span style='font-family:Arial; font-size:12pt'><strong>La aceleración será positiva cuando:<br /></strong></span></div><p><span style='font-family:Arial; font-size:12pt'>*La velocidad es de signo positivo y experimenta un aumento<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>*la velocidad es de signo negativo y sufre una disminución, es decir, un frenado.<br /></span></p></li><li><div><span style='font-family:Arial; font-size:12pt'>La aceleración es negativa cuando:<br /></span></div><p><span style='font-family:Arial; font-size:12pt'>*la velocidad es de signo negativo y tiene un aumento<br /></span></p><p><br /> </p></li></ul><p><br /> </p><p><span style='color:#00b050; font-family:Arial; font-size:14pt'><strong>Ejercicios propuestos del M. R. U. V <br /></strong></span></p><p><span style='font-family:Arial; font-size:12pt'>Un automóvil adquiere una velocidad de 40 km/h al sur en 4 s ¿cual es su aceleración en m/s? <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Datos: formulas conversión sustitución <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>v= 40 km/h a = <span style='text-decoration:underline'>v <br /></span></span></p><p><span style='font-family:Arial; font-size:12pt'>t= 4 s t 1 <span style='text-decoration:underline'>km</span>= <span style='text-decoration:underline'>1000 m </span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'>a= h 3600s<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> 40 <span style='text-decoration:underline'>km </span> = x a= <span style='text-decoration:underline'>11.11 m/s<br /></span></span></p><p><span style='font-family:Arial; font-size:12pt'> h 4 s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> X = (<span style='text-decoration:underline'>40 km</span>) (<span style='text-decoration:underline'>1000m)<br /></span></span></p><p><span style='font-family:Arial; font-size:12pt'> h 3600s a = 2.77 m/s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> 1 <span style='text-decoration:underline'>km</span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'> h<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> x = 11.111 m/s <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Determina la rapidez que llevará un ciclista a los 5 s, si al bajar por una pendiente adquiere una aceleración de 1.5 m/s y parte con una rapidez inicial de 3 m/s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Datos: formula sustitución <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> t: 5 s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> a: 1.5 m/s vf= vo + at vf= 3 m/s + 1.5 m/s (5 s)<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Vo: 3 m/s vf= 3m/s + 7.5 m/s <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Vf: vf= 10.5 m/s <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Un móvil tiene una velocidad inicial de 4m/s al sur y experimenta una aceleración de 2 m/s la cual dura 12 s. calcular:<br /></span></p><ol><li><span style='font-family:Arial; font-size:12pt'>que desplazamiento tiene a los 12 s<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>que velocidad lleva a los 12 s <br /></span></li></ol><p><span style='font-family:Arial; font-size:12pt'>Datos: formulas: sustitución <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> Vo: 4 m/s al sur d: (4m/s x 12s) + (2m/s) (12s)<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> a: 2 m/s d: vo t + at <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> t: 12 s 2<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> d: d: 48 m + 144 m <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> vf: vf: vo + at d: 192 m al sur<br /></span></p><p><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>vf: 4 m/s + (2m/s x 12s)<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> vf: 4m/s +24 m <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> VF: 28 m/s al sur <br /></span></p><p><span style='color:blue; font-family:Arial; font-size:14pt'><strong>Aceleración media <br /></strong></span></p><p><span style='font-family:Arial; font-size:12pt'>Cuando un móvil varía su velocidad es necesario determinar su aceleración media aplicando la siguiente formula.<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'> am: vf- vo<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> tf- to<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Ecuaciones para calcular desplazamiento<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- d: vot + <span style='text-decoration:underline'>at</span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'> 2<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>2.- vf – vo<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> 2 a <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>3.- d: vf + vo t <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> 2 <br /></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Cuando la velocidad inicial vale cero las tres ecuaciones anteriores se reducen a las siguientes:<br /></span></p><p><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>1. - d. - at<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>2<br /></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>2. - d. vf<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'> 2 a <br /></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>3. - d: vf<br /></span></p><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'>2 t<br /></span></p><p style='text-align: center'><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Ecuaciones para calcular velocidades finales:<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- vf: vo + at <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>2.- vf: vO + 2 at <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Si la velocidad es cero las ecuaciones anteriores se reducen a las siguientes expresiones.<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- vf: at<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>2.- vf: 2 ad <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Ejercicios:<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>1.- determina la velocidad media de un móvil que lleva una velocidad inicial de 3 m/s y su velocidad final es de 4.2 m/s<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Datos: formula sustitución <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Vo: 3m/s vm: <span style='text-decoration:underline'>3m/s + 4.2 m/s</span><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'>Vf: 4.2 m/s vm: <span style='text-decoration:underline'>vo + vf</span> 2 <br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Vm:? 2 Vm: 3.6 m/s <br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>2.- calcular el tiempo en horas en que un automóvil recorre una distancia de 3 km si lleva una velocidad media de 50 km/h al sur<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>Datos: formulas sustitucion <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> d: 3 km<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>vm: 50 km/h t: d t: 3 km<br /></span></p><p><span style='font-family:Arial; font-size:12pt'> t: vm 50 km/h<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'> Vm: d t: 0.06 h <br /></span></p><p><span style='font-family:Arial; font-size:12pt'> t<br /></span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'><br /> </span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:14pt'><strong>CAIDA LIBRE<br /></strong></span></p><p style='text-align: center'><br /> </p><p><span style='font-family:Arial; font-size:14pt'><strong>Definición<br /></strong></span></p><p><br /> </p><ul><li><span style='font-family:Arial; font-size:12pt'>Se define como la caída de un cuerpo sobre la superficie de la tierra sin ninguna resistencia originada por el aire.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Todos los cuerpos ya sean grandes o pequeños, en ausencia de fricción caen a la tierra con la misma aceleración<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La aceleración gravitacional produce sobre los cuerpos con caída libre un movimiento uniforme variado.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>En caída libre la velocidad aumenta en forma constante y la aceleración permanece fija <br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La aceleración de la tierra es de 9.8 m/s<sup>2. </sup>Es una magnitud vectorial cuya dirección esta dirigida hacia el centro de la tierra, por lo que su valor debe ser negativo.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La aceleración de la tierra se representa con la letra "g"<br /></span></li><li><div><span style='font-family:Arial; font-size:12pt'>Para resolver problemas de caída libre se utilizan las mismas ecuaciones de MRUV, pero se cambia la letra a de aceleración por g que representa la aceleración de la gravedad y la letra "d" de distancia por "h" que representa la altura<br /></span></div><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p></li></ul><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><span style='font-family:Arial; font-size:14pt'><strong>TIRO VERTICAL<br /></strong></span></p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p style='text-align: center'><br /> </p><p><br /> </p><p style='margin-left: 25pt'><span style='font-family:Arial; font-size:12pt'><strong>TIRO VERTICAL<br /></strong></span></p><p style='margin-left: 25pt'><br /> </p><ul><li><span style='font-family:Arial; font-size:12pt'>Es el movimiento de un cuerpo que se lanza verticalmente hacia arriba observándose que su velocidad va disminuyendo hasta anularse cuando alcanza su máxima altura.<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>El tiempo empleado en subir, es el mismo utilizado en bajar<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>El tiro vertical sigue las mismas leyes de la caída libre de los cuerpos, por tanto, emplea las mismas ecuaciones<br /></span></li><li><div><span style='font-family:Arial; font-size:12pt'>Para calcular la altura máxima que alcanza un cuerpo, se utiliza las siguientes ecuaciones:<br /></span></div><p> <br /> </p></li></ul><p style='text-align: center'><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><ul><li><div><span style='font-family:Arial; font-size:12pt'>Para calcular el tiempo que tarda en subir utilizamos la ecuación:<br /></span></div><p><br /> </p></li></ul><p><br /> </p><p> <br /> </p><p><br /> </p><p style='margin-left: 25pt'><br /> </p><ul><li><div><span style='font-family:Arial; font-size:12pt'>Como el tiempo que tarda en subir es el mismo para bajar entonces el tiempo de permanencia en el aire será:<br /></span></div><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>EJERCICIOS PROPUESTOS DE TIRO VERTICAL</span><br /> </p></li></ul><p><span style='color:#000045; font-family:Arial; font-size:12pt'>Se lanza un cuerpo verticalmente hacia arriba con una velocidad inicial de 100 m/s, luego de 4 s de efectuado el lanzamiento su velocidad es de 60 m/s.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>a) ¿Cuál es la altura máxima alcanzada?.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>b) ¿En qué tiempo recorre el móvil esa distancia?.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>c) ¿Cuánto tarda en volver al punto de partida desde que se lo lanzo?.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>d) ¿Cuánto tarda en alcanzar alturas de 300 m y 600 m?.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>Usar g = 10 m/s ².<br /></span></p><p style='margin-left: 2pt'><br /> </p><p style='margin-left: 2pt'><span style='color:#000033; font-family:Arial; font-size:12pt; text-decoration:underline'><strong>DESARROLLO<br /></strong></span></p><p style='margin-left: 6pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><em>Datos</em>:<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>v<sub>0</sub> = 100 m/s<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>v<sub>f</sub> = 60 m/s<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>t = 4 s<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>y<sub>1</sub> = 300 m<br /></span></p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>y<sub>2</sub> = 600 m<br /></span></p><p style='margin-left: 36pt'><br /> </p><p style='margin-left: 36pt'><span style='color:#000045; font-family:Arial; font-size:12pt; text-decoration:underline'><strong>FORMULAS<br /></strong></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>A ) v<sub>f</sub> = v<sub>0</sub> + g.t<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>B) y = v<sub>0</sub>.t + g.t ²/2<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>C) v<sub>f</sub> ² - v<sub>0</sub> ² = 2.g.h<br /></span></p><p style='margin-left: 3pt'> <br /> </p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt; text-decoration:underline'><strong>SUSTITUCION<br /></strong></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'> a) Para la altura máxima v<sub>f</sub> = 0, de la ecuación (3):<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>-v<sub>0</sub> ² = 2.g.h<br/>h<sub> máx</sub> = -v<sub>f</sub> ²/(2.g)Þ h<sub> máx</sub> = -(100 m/s) ²/[2.(-10 m/s ²)]<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>h<sub> máx</sub> = 500 m<br /></strong></span></p><p style='margin-left: 3pt'><br /> </p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>b) De la ecuación (1) y para v<sub>f</sub> = 0:<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>t = v<sub>0</sub>/g<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>t = (-100 m/s)/(-10 m/s ²)<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>t = 10 s<br /></strong></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>c) Recordemos que en tiro vertical, cuando un objeto es lanzado hacia arriba y luego cae, cuando vuelve a pasar por el punto de partida posee la misma velocidad que en el momento del lanzamiento <strong>pero con sentido contrario</strong> (v<sub>f</sub> = -v<sub>0</sub>).<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>Podemos asegurar que el resultado pedido es el doble del tiempo que requirió para alcanzar la altura máxima.<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>t = 20 s</strong><br /> </span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>e) No puede alcanzar una altura de 600 m porque la máxima es de 500 m. Para h = 300 m empleamos la ecuación (2):<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>0 = v<sub>0</sub>.t + g.t ²/2 - y<br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'>Aplicamos la ecuación cuadrática que dará dos resultados: <br /></span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>t<sub>1</sub> = 3,68 s</strong><br /> </span></p><p style='margin-left: 3pt'><span style='color:#000045; font-family:Arial; font-size:12pt'><strong>t<sub>2</sub> = 16,32 s</strong><br /> </span></p><p style='margin-left: 3pt'><br /> </p><p style='text-align: center'><span style='font-family:Arial Narrow; font-size:18pt'><strong>Tiro parabólico oblicuo<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Tiro parabólico oblicuo. Se caracteriza por la trayectoria que sigue un cuerpo cuando es lanzado con una velocidad inicial que forma un ángulo con el eje horizontal.<br /></span></p><p style='text-align: center; margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><br /> </span></p><p><span style='font-family:Arial; font-size:12pt'>1.- Un jugador le pega a una pelota con un ángulo de 37° con respecto al plano horizontal, comunicándole una velocidad inicial de 15 m/seg. Calcular a) e tiempo que dura en el aire, b) La altura máxima alcanzada, c) El alcance horizontal de la pelota.<br /></span></p><p style='margin-left: 18pt'><br /> </p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Datos Fórmulas Sustitución<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Vo = 15 m/seg Vov = Vo sen θ Vov = 15 m/seg x sen 37°<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>θ= 37° VH = Vo cos θ Vov = 15 m/seg x 0.6018<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>g = -9.8 m/seg2. t (aire) = - 2Vov/g Vov = 9.027 m/seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>t (aire) = ? h max = - V2ov/2g VH = 15 m/se x cos 37°<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>h max= ? dH = VH t (aire) VH = 15 m/seg x 0.7986<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>dH= ? VH = 11.979 m/seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> t aire= - <span style='text-decoration:underline'>2 (9.027 m/seg)</span><strong><br /> </strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><strong> </strong>-9.8 m/seg2.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> <strong>t aire = 1.842 seg<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><strong> </strong>h max = - <span style='text-decoration:underline'>(9.027 m/seg)2 =</span><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> 2 (- 9.8 m/seg2.)<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> <strong>h max = 4.157 metros<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><strong> </strong>dH = 11.979 m/seg x 1.842 seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> <strong>dH = 22.06 metros<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>2.- Un proyectil se lanza con una velocidad inicial de 200 m/seg si se desea que dé en un blanco localizado a 2500 metros, calcular: a) El ángulo con el cual debe ser lanzado b) el tiempo que tarda en llegar al blanco (tiempo en el aire).<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Datos Fórmulas Sustitución<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>Vo = 200 m/seg - sen 2 θ= <span style='text-decoration:underline'>dHg</span> - sen 2 θ= <span style='text-decoration:underline'>2500 m x(- 9.8 m/seg2)</span>.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>dH = 2500 m Vo2. (200 m/seg)2.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>g = -9.8 m/seg2. Vov = Vo sen θ sen 2 θ = 0.6127<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>a) θ= t (aire)= -<span style='text-decoration:underline'>2Vov </span> 2 θ = ángulo cuyo seno es g 0.6127 <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'>b) t aire =? 2 θ= 37.76°<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> <strong>θ= 18.88°<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'><strong> Vov = </strong>200 m/seg x sen 18.88°<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> Vov = 200 m/seg x 0.3230= 64.6 m/seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> t (aire) = - <span style='text-decoration:underline'>2 x 64.6 m/seg = </span><strong>13.18 seg</strong><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial; font-size:12pt'> - 9.8 m/seg2.<br /></span></p><ul><li><span style='font-family:Arial; font-size:12pt'>3.- ¿Cuál será la velocidad inicial con que se batea una pelota de beisbol, si es golpeada con un ángulo de 40° respecto a la horizontal, si la altura máxima que alcanza es de 10.2 metros y su desplazamiento horizontal es de 48.62 metros?<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Datos Fórmula<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Vo = ? dH = -<span style='text-decoration:underline'> Vo2 sen 2 θ <br /></span></span></li><li><span style='font-family:Arial; font-size:12pt'>Θ = 40° g<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>h max = 10.2 m despejando Vo tenemos:<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>dH = 48.62 m Vo = √<span style='text-decoration:underline'>dHg<br /></span></span></li><li><span style='font-family:Arial; font-size:12pt'>g = -9.8 m/seg2. sen 2 θ<br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Sustitución y resultado:<br /></span></li><li><div><span style='font-family:Arial; font-size:12pt'>Vo = √ <span style='text-decoration:underline'>48.62 m x -9.8 m/seg2. </span> = √<span style='text-decoration:underline'> 476.476 m2/s2.<br /></span></span></div><ul style='margin-left: 108pt'><li><span style='font-family:Arial; font-size:12pt'>sen (80°) 0.9848<br /></span></li></ul></li><li><span style='font-family:Arial; font-size:12pt'>Vo = <strong>22 m/seg</strong>.<br /></span></li></ul><p><br /> </p><p><br /> </p><p><br /> </p><p style='text-align: center; margin-left: 3pt'><span style='font-family:Arial; font-size:12pt'><strong>TIRO PARABOLICO<br /></strong></span></p><p style='margin-left: 3pt'><br /> </p><p><span style='font-size:12pt'>Se denomina <strong>tiro parabólico</strong> al realizado por un objeto cuya trayectoria describe una <a title='Parábola (matemática)' href='http://es.wikipedia.org/wiki/Par%C3%A1bola_(matem%C3%A1tica)'>parábola</a>. Se corresponde con la trayectoria ideal de un <a title='Proyectil' href='http://es.wikipedia.org/wiki/Proyectil'>proyectil</a> que se mueve en un medio que no ofrece resistencia al avance y que está sujeto a un <a title='Campo gravitatorio' href='http://es.wikipedia.org/wiki/Campo_gravitatorio'>campo gravitatorio</a> uniforme.<br /></span></p><p><span style='font-size:12pt'>Puede ser analizado como la composición de dos movimientos rectilíneos: un <a title='Movimiento rectilíneo uniforme' href='http://es.wikipedia.org/wiki/Movimiento_rectil%C3%ADneo_uniforme'>movimiento rectilíneo uniforme</a> horizontal y un <a title='Movimiento rectilíneo uniformemente acelerado' href='http://es.wikipedia.org/wiki/Movimiento_rectil%C3%ADneo_uniformemente_acelerado'>movimiento rectilíneo uniformemente acelerado</a> vertical.<br /></span></p><div><table border='0' style='border-collapse:collapse'><colgroup><col style='width:54px'/></colgroup><tbody valign='top'><tr><td style='padding-top: 1px; padding-left: 1px; padding-bottom: 1px; padding-right: 1px' vAlign='middle'><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'><br /> </span> </p></td></tr></tbody></table></div><h2><span style='font-family:Arial; font-size:12pt'>Tipos de movimiento parabólico <br /></span></h2><p style='text-align: center'><span style='font-family:Arial; font-size:12pt'><br /> </span></p><p><br /> </p><p><span style='font-family:Arial; font-size:12pt'>Movimiento de media parábola<br /></span></p><p><span style='font-family:Arial; font-size:12pt'>El movimiento de media parábola o semiparabólico (lanzamiento horizontal) <br /></span></p><ul><li><span style='font-family:Arial; font-size:12pt'>Se puede considerar como la composición de un avance horizontal rectilíneo uniforme y la <a title='Caída libre' href='http://es.wikipedia.org/wiki/Ca%C3%ADda_libre'>caída libre</a>. <br /></span></li></ul><p><span style='font-family:Arial; font-size:12pt'>El movimiento parabólico completo <br /></span></p><ul><li><span style='font-family:Arial; font-size:12pt'>Se puede considerar como la composición de un avance horizontal rectilíneo uniforme y un lanzamiento vertical hacia arriba, que es un movimiento rectilíneo uniformemente acelerado hacia abajo (MRUA) por la acción de la <a title='Gravedad' href='http://es.wikipedia.org/wiki/Gravedad'>gravedad</a>. <br /></span></li></ul><p><span style='font-size:12pt'>En condiciones ideales de resistencia al avance nulo y campo gravitatorio uniforme, lo anterior implica que:<br /></span></p><ol><li><span style='font-family:Arial; font-size:12pt'>Un cuerpo que se deja caer libremente y otro que es lanzado horizontalmente desde la misma <a title='Alto dimensional' href='http://es.wikipedia.org/wiki/Alto_dimensional'>altura</a> tardan lo mismo en llegar al suelo. <br /></span></li><li><span style='font-family:Arial; font-size:12pt'>La independencia de la <a title='Masa' href='http://es.wikipedia.org/wiki/Masa'>masa</a> en la caída libre y el lanzamiento vertical es igual de válida en los movimientos parabólicos. <br /></span></li><li><span style='font-family:Arial; font-size:12pt'>Un cuerpo lanzado verticalmente hacia arriba y otro parabólicamente completo que alcance la misma altura tarda lo mismo en caer. <br /></span></li></ol><h2><span style='font-family:Arial; font-size:12pt'>Ecuaciones del tiro parabólico <br /></span></h2><p><br /> </p><p><span style='font-size:12pt'>Hay dos ecuaciones que rigen el tiro parabólico:<br /></span></p><ol><li><span style='font-family:Arial; font-size:12pt'><br /> </span></li><li><span style='font-family:Arial; font-size:12pt'><br /> </span></li></ol><p><span style='font-size:12pt'>Donde:<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>es el módulo de la velocidad inicial. <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>es el ángulo de la velocidad inicial sobre la horizontal. <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>es la aceleración de la gravedad. <br /></span></p><p><span style='font-size:12pt'>La velocidad inicial se compone de dos partes:<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>que se denomina componente horizontal de la velocidad inicial. <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>En lo sucesivo <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>que se denomina componente vertical de la velocidad inicial. <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'>En lo sucesivo <br /></span></p><p><span style='font-size:12pt'>Se puede expresar la velocidad inicial de este modo:<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial; font-size:12pt'> : [ecu. 1] <br /></span></p><p><span style='font-size:12pt'>Será la que se utilice, excepto en los casos en los que deba tenerse en cuenta el ángulo de la velocidad inicial.<br /></span></p><p><br /> </p><p><br /> </p><p style='text-align: center'><span style='font-size:16pt'><strong>Tiro horizontal<br /></strong></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>Tiro parabólico horizontal. Se caracteriza por la trayectoria o camino curvo que sigue un cuerpo al ser lanzado horizontalmente al vacío, resultado de dos movimientos independientes: un movimiento horizontal con velocidad constante y otro vertical, el cual se inicia con una velocidad cero y va aumentando en la misma proporción de otro cuerpo que se dejará caer del mismo punto en el mismo instante. <br /></span></p><p><span style='font-family:Arial Narrow; font-size:14pt'> EJERCICIOS PROPUESTOS<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>1- Se lanza una piedra horizontalmente con una velocidad de 25 m/seg desde una altura de 60 metros. Calcular: a) el tiempo que tarda en llegar al suelo, b) la velocidad vertical que lleva a los 2 segundos, c) La distancia horizontal a la que cae la piedra.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>Datos Fórmulas Sustitución<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> ____ _________________<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>VH = 25 m/seg a) t caer = √2h/g t caer = √2 (-60 m)/-9.8 m/seg2.<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>h = -60 metros b) V2 seg= g t <strong>t caer = 3.5 seg</strong><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>g= - 9.8 m/seg2. <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> V2seg = -9.8 m/seg2x 2 seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>a) t caer =? c) dH= VH t <strong>V2 seg= - 19.6 m/seg</strong><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>b) V2 seg= ? dH= 25 m/seg x 3.5 seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>c) dH= ? <strong>dH = 87.5 metros </strong><br /> </span></p><p><br /> </p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>2.- Una pelota es lanzada horizontalmente desde una ventana con una velocidad inicial de 10 m/seg y cae al suelo después de 5 segundos: Calcular a) ¿ A qué altura se encuentra la ventana? b) ¿A qué distancia cae la pelota?<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>Datos Fórmulas Sustitución<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>VH = 10 m/seg a) h = gt2/2 a) h =<span style='text-decoration:underline'> -9.8 m/seg2x (5 seg)2<br /></span></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>t caer = 5 seg 2 <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> b) dH = VHtcaer <br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>g = -9.8 m/seg2. a) <strong>h = -122.5 metros</strong><br /> </span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>a) h = ? b) dH = 10 m/seg x 5 seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>b) dH =? b) <strong>dH = 50 metros</strong><br /> </span></p><p><br /> </p><p><span style='font-family:Arial Narrow; font-size:14pt'>3.- Un avión vuela horizontalmente con una velocidad de 800 km/h y deja caer un proyectil desde una altura de 500 m respecto al suelo. Calcular: a) ¿Cuánto tiempo transcurre antes de que el proyectil se impacte en el suelo? b) ¿Qué distancia horizontal recorre el proyectil después de iniciar su caída?<br /></span></p><p><span style='font-family:Arial Narrow; font-size:14pt'> Datos Fórmulas <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>VH = 800 km/h a) t (caer) = √2h/g <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'>h = -500 m b) dH = VH t (caer.)<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>g = -9.8 m/seg2. Sustitución y resultados.<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>a) t(caer)=? a) t (caer) = √2 (-500 m)/ -9.8 m/seg2. <br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> b) dH = ? a) t( caer) = 10.10 seg.<br /></span></p><p><br /> </p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>Conversión de km/h a m/seg:<br /></span></p><p style='margin-left: 36pt'><span style='font-family:Arial Narrow; font-size:14pt'>800 <span style='text-decoration:underline'>km</span> x <span style='text-decoration:underline'>1000 m</span> x <span style='text-decoration:underline'> 1 h </span>= 222.22 m/seg<br /></span></p><p style='margin-left: 18pt'><span style='font-family:Arial Narrow; font-size:14pt'> h 1 km 3600 seg<br /></span></p><p> <br /> </p><ol><li><span style='font-family:Arial Narrow; font-size:14pt'>dH = 222.22 m/seg x 10.10 seg = 2244.42 m<br /></span></li></ol><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:#993300'><strong><em>IMPORTANCIA DEL ESTUDIO DE LA CINEMATICA.</em><br /> </strong></span></p><ul><li><span style='color:#3366ff'>Permite conocer y predecir en qué lugar se encontrará un cuerpo, qué velocidad <br /></span></li><li><span style='color:#3366ff'>tendrá al cabo de cierto tiempo o en lapso llegará a su destino.<br /></span></li><li><span style='color:#3366ff'>Permite hacer la descripción del movimiento de un cuerpo.<br /></span></li><li><span style='color:#3366ff'>Permite precisar a cada instante, la posición de una partícula en el espacio.<br /></span></li></ul><p><br /> </p><p><span style='color:#ff6600'><strong><em>CONCEPTO DE PARTICULA MATERIAL EN MOVIMIENTO<br /></em></strong></span></p><p><span style='color:#99cc00'><strong>Movimiento.-</strong> Es la variación de la posición de una partícula respecto a un punto considerado fijo.<br /></span></p><p><span style='color:#99cc00'><strong>Partícula Material en Movimiento.- Es cualquier objeto material o cuerpo físico en movimiento.<br /></strong></span></p><p><strong>Ejemplo:<br /></strong></p><p> <br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:#99cc00'><strong>La trayectoria<br /></strong></span></p><p><span style='color:#99cc00'><strong>de una partícula <br /></strong></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:red'><strong><em>SISTEMAS DE REFERENCIAS.</em><br /> </strong></span></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:#99cc00'><strong>Para describir la posición de una partícula se utiliza un sistema de coordinadas.<br /></strong></span></p><ul><li>El eje se corta perpendicularmente en un punto 0 llamado origen.<br /></li><li>El eje horizontal es el eje de las abscisas o de las <em>x</em><br /> </li><li>El eje vertical es el eje de las ordenadas o de las <em>y</em><br /> </li></ul><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='font-family:Arial Narrow'>La posición de M está determinada por dos magnitudes:<br /></span></p><p style='margin-left: 70pt'><span style='font-family:Arial Narrow'>La abscisa 0 Q y la Ordenada 0 P<br /></span></p><p><span style='font-family:Arial Narrow'>La posición de de la partícula es:<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'>M = (x, y)<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'>Donde: x = 40<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'> y = 30<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'>Por lo tanto:<br /></span></p><p style='margin-left: 35pt'><span style='font-family:Arial Narrow'> M = (40, 30)<br /></span></p><p><span style='font-family:Arial Narrow'>La posición de M también puede representarse por el vector es llamado <strong>vector de <br /></strong></span></p><p><span style='font-family:Arial Narrow'><strong> Posición, </strong>cuyos componentes rectangulares son<strong> x, y.<br /></strong></span></p><p><span style='font-family:Arial Narrow'><strong>Según el cuadrante en que se encuentren las coordenadas, éstas tendrán signo positivo o negativo, según la posición de la partícula.<br /></strong></span></p><p><strong><br /> </strong></p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:#999999'><strong><em>DISTANCIA, DESPLAZAMIENTO, VELOCIDAD Y RAPIDEZ.<br /></em></strong></span></p><p><strong>Distancia:<br /></strong></p><ul><li>Es la longitud que recorre un móvil sin importar la dirección del recorrido.<br /></li><li>Es una magnitud escalar.<br /></li></ul><p><br /> </p><ul><li><strong>Desplazamiento<br /></strong></li><li>Es la distancia medida en una dirección particular entre dos puntos: el de partida y el de llegada.<br /></li><li>Es una magnitud vectorial.<br /></li></ul><p><br /> </p><ul><li><strong>Rapidez.<br /></strong></li><li>Es una magnitud escalar que relaciona la distancia recorrida con el tiempo. velocidad.<br /></li><li><br /> </li></ul><p><br /> </p><ul><li><strong>Velocidad.</strong><br /> </li><li>Es una magnitud vectorial.<br /></li><li>Es la rapidez con que se mueve un cuerpo.<br /></li><li>Es una magnitud vectorial que relaciona el cambio de posición (o desplazamiento) con el tiempo. <br /></li></ul><p><br /> </p><p><br /> </p><p><br /> </p><p><span style='color:purple; font-family:Arial; font-size:14pt'><br /> </span> </p></span>Karlahttp://www.blogger.com/profile/05031254835401085216noreply@blogger.com0