A train is moving at a constant speed on a track parallel to a road. As the front of the train passes a stopped car, the car starts accelerating at a constant rate. When the back of the train catches up to the car, the car is moving as fast as the train. As the car continues to accelerate, it catches up to the front of the train right when the car reaches the speed limit.

Express the distance traveled in terms of the length of the train.
Express the speed limit in terms of the speed of the train.

Formulas:
distance = speed * time
distance = (1/2) * acceleration * time^2
speed = time * acceleration