AS Daily A Level Physics question
Two cyclists start together from rest on a straight path. Cyclist A accelerates uniformly at a for a time T. Cyclist B accelerates uniformly at 2a for a time T/2. Neglect resistive forces. Which statement must be true at the moments they stop accelerating?
Answer
The correct answer is D.
Correct: D — They have the same final speed, and A has travelled farther. A B accelerates harder but for a shorter time; the larger acceleration does not make his final speed greater here because speed change depends on acceleration multiplied by time, and those products are equal, and his shorter time reduces distance. B Equal final speed is correct, but B does not go farther; for uniform acceleration from rest, distance grows strongly with time, so the shorter time means B covers less distance. C B’s final speed is not smaller; with equal acceleration–time products the final speeds match, and the distances are not the same because the times differ. D Same final speed follows from equal acceleration × time, and A’s longer acceleration time gives a larger distance because distance increases more with time than with acceleration in this comparison.