Question

As a traffic light turns green, a waiting car starts with a constant acceleration of 6.0 m/s^2. At the instant the car begins to accelerate, a truck with a constant velocity of 21 m/s passes in the next lane.

A)How far will the car travel before it overtakes the truck?

B)How fast will the car be travelling when it overtakes the truck?

Answer 1

Write equations for the distance from the traffic light vs time for each car. Measure time from when they leave the light.
X1 = 3 t^2
X2 = 21 t

Set X1 = X2 and solve for t. Take the nonzero solution. Use that t and either equation to get the location. The velocity of the car at that time will be 6.0 * t. I expect it will be 42 m/s, since it will have to have the same average velocity as the truck at that time.

Answer 2

36.75