Question

The car with an irresponsible driver starts to brake when it goes through a red light. When passing the traffic light, he does so at a speed of 115 kph in the right lane. Further ahead, 70 meters from the traffic light, a child is crossing the street and falls. If the effect of the car's brakes is equivalent to a deceleration of magnitude 5.7m/s². Is the child hit by the car or not? How far from the traffic light does the car stop?

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Answer to a math question The car with an irresponsible driver starts to brake when it goes through a red light. When passing the traffic light, he does so at a speed of 115 kph in the right lane. Further ahead, 70 meters from the traffic light, a child is crossing the street and falls. If the effect of the car's brakes is equivalent to a deceleration of magnitude 5.7m/s². Is the child hit by the car or not? How far from the traffic light does the car stop?

Expert avatar
Darrell
4.5
99 Answers
Solución: La distancia x desde un punto fijo de un objeto en el tiempo t está dada por x\left(t\right)=\frac{1}{2}a_0t^2+v_0t+x_0 donde a_0, v_0 y x_0 son la aceleración, velocidad y posición iniciales en t=0. Mientras tanto, la velocidad de un objeto en el tiempo t está dada por v\izquierda(t\derecha)=a_0t+v_0 Convirtiendo la velocidad inicial de kph a m/s, 115kph\times\frac{1000m}{1km}\times\frac{1hr}{3600s} =\frac{575}{18}m/s Para encontrar el tiempo que tarda el vehículo en detenerse, resuelve t usando la función de velocidad v\left(t\right)=-5.7t+\frac{575}{18}=0 5.7t=\frac{575}{18} t\aproximadamente 5,6s Estableciendo el punto inicial como el semáforo y sustituyendo valores conocidos, x\left(5.6\right)=\frac{1}{2}\left(-5.7\right)\left(5.6\right)^2+\left(\frac{575}{18}\right )\izquierda(5.6\derecha)+0 x\izquierda(5.6\derecha)\aprox89.5m{>}70m Por tanto, el niño es atropellado y el coche se detiene a unos 89,5 metros del semáforo. Respuesta: Como el coche se detiene a unos 89,5 metros del semáforo, el coche atropella al niño.

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