Two identical cars, A and B, are fitted with the same brake system that produces a constant uniform retardation whenever applied. Car A is moving at 60km h−1 and car B at 30km h−1 on a straight, level road when their drivers apply the brakes at the same instant.
(i) Show, by calculation, that the ratio of the stopping distance of car A to that of car B is 4:1.
(ii) In a separate trial with the same brakes, a car travelling at 15m s−1 comes to rest in 45m. Calculate the magnitude of the retardation produced by the brakes.
(iii) Using your answer to part (ii), estimate the distance required to stop the same car if its initial speed is doubled. Comment on how stopping distance depends on the initial speed.