AS Daily A Level Physics question
A trolley moves to the right along a straight, level track. At t = 0 it has a positive velocity, and a constant braking force then produces a uniform acceleration to the left. You consider the trolley’s displacement from its start point measured at a chosen end time T, where T is allowed to extend beyond the instant the trolley first comes to rest and reverses. Which statement must be true about how the displacement depends on T?
Answer
The correct answer is B.
Correct: B — It increases up to the instant the trolley first comes to rest, then decreases as T increases further. A velocity–time graph has positive velocity before the stop (adding positive area/displacement) and negative velocity after (adding negative area), so the net displacement grows to a maximum at the stop and then is reduced by the growing negative area; in the limit of a tiny time after the stop, the new negative area is tiny, so the displacement is still positive but smaller. A is wrong because constant acceleration does not make displacement increase monotonically; once velocity is negative, additional time subtracts from the earlier positive displacement. B is correct as explained by the sign change of velocity and the limiting case just after the stop. C is wrong because at the instant of first coming to rest there has been no negative-velocity motion yet, so nothing has cancelled; that instant actually marks the maximum forward displacement. D is wrong because the displacement does not flip negative immediately after reversal; it only becomes negative after sufficient time for the accumulated negative area to exceed the earlier positive area.