Where will the automobile overtake the truck?

Question

At the instant the traffic light turns green, an automobile that has been waiting at an intersection starts ahead with a constant acceleration of 86 m/s². at the same instant, a truck, traveling with a constant speed of 44 m/s overtakes and passes the automobile.

How far beyond its starting point does the automobile overtake the truck?

Answer

After t seconds, the truck's distance to the traffic light is 44 t.

After t second the automobile's distance to the traffic light is 86 t² /2.

The automobile will overtake the truck when both are at an equal distance to traffic light. That happens at time t where t solves

By that time, the truck (and the automobile) will be at a distance d from the traffic light, where d is

So the answer is d metres.

Retry