Question

A car capable of a constant acceleration of 3.72 m/s^2 is stopped at a traffic light. When the light turns green, the car starts from rest with this acceleration. At the very same moment, a truck traveling with constant velocity 13.8 m/s passes the car. As the car’s velocity increases, it will eventually move faster than the truck and later overtake it. How far from the light will the car catch up with the truck?

Answer 1

Step-by-step explanation:

Let t be the time it takes for the car to catch up with the truck.

Using kinematics equations,

Distance by car = ut + 0.5at² = 0 + 0.5 * 3.72 * t².

Distance by truck = 13.8 * t.

Since these distances have to be equal, we have:

0.5 * 3.72 * t² = 13.8t, 1.86t² = 13.8t, t ≈ 7.42s.

Hence the distance is 13.8 * (7.42) ≈ 102.4m.