AS Daily A Level Physics question
Two runners move straight along a track for a total time 2t. Runner A starts from rest, accelerates uniformly to speed v during the first t seconds, then continues at speed v for the next t seconds. Runner B runs at a constant speed v for the whole 2t. Which statement must be true about the distances they cover in the 2t interval?
Answer
The correct answer is C.
Correct: C — Runner A covers 25% less distance than Runner B. A uniform acceleration from 0 to v over t gives an area (displacement) of 0.5·v·t, then constant v for t adds v·t, totaling 1.5·v·t; Runner B’s constant v for 2t gives 2·v·t, so Runner A’s distance is 1.5/2 = 0.75 of Runner B’s (25% less). A They are not the same: 1.5·v·t ≠ 2·v·t. B This reverses the ratio; the accelerate-then-cruise profile gives less area than constant v for the same total time. C As shown, 1.5·v·t vs 2·v·t implies 25% less, not more or equal. D Average speed differs: Runner A’s average is (1.5·v·t)/(2t) = 0.75v, which is less than Runner B’s v.