Two identical cars A and B are fitted with the same braking system. Car A is moving with a speed of 54km h−1 while car B is moving with a speed of 72km h−1.
(a) Assuming the maximum available retardation is the same for both cars, find the ratio of their respective stopping distances.
(b) Before braking, car A is 25m behind car B and both are travelling at 54km h−1. Suddenly, car B accelerates uniformly to 72km h−1 in 4s and then immediately applies maximum braking until it stops. Car A continues at 54km h−1 for a reaction time of 1s and then also applies maximum braking. Show by calculation whether car A will collide with car B. Take the maximum retardation as 4m s−2.