Question

A bus travelling at 72 km /h sees a child and suddenly stops. The time taken to stop is 10 seconds. How do you calculate the acceleration and the distance traveled before coming to a rest?

Answer 1

To calculate the acceleration and distance traveled by the bus before coming to a rest, we can use the following equations of motion:

1. Acceleration (a): a = (final velocity - initial velocity) / time

2. Distance (d): d = (initial velocity * time) + (0.5 * acceleration * time^2)

Given: Initial velocity (u) = 72 km/h (convert to m/s by dividing by 3.6: 72/3.6 = 20 m/s) Final velocity (v) = 0 m/s (since the bus comes to rest) Time (t) = 10 seconds

1. Acceleration: a = (v - u) / t = (0 - 20) / 10 = -2 m/s^2

The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, representing deceleration or slowing down.

2. Distance: d = (u * t) + (0.5 * a * t^2) = (20 * 10) + (0.5 * -2 * 10^2) = 200 + (-100) = 100 meters

Therefore, the acceleration of the bus is -2 m/s^2 (deceleration) and the distance traveled before coming to a rest is 100 meters.