Two identical cars, A and B, are moving along the same straight road in the same direction. Car A is travelling at 15m s−1 while car B, 120m behind A, is travelling at 30m s−1. At a certain instant both drivers see an obstacle ahead and apply their brakes simultaneously. The magnitude of the uniform retardation produced is the same for the two cars and equals 4.0m s−2.
a. (i) For each car, obtain an expression for its stopping distance in terms of its initial speed u and the common retardation a.
b. (ii) Calculate the stopping distances for cars A and B.
c. (iii) Determine whether car B collides with car A before both cars come to rest. Support your answer with suitable numerical evidence.