AS Daily A Level Physics question
On a straight test track, two cars start from rest. Car X accelerates uniformly at 2.0 m/s^2 for 10 s. Car Y accelerates uniformly at 4.0 m/s^2 for 5.0 s. Ignore resistive forces. Which statement must be true?
Answer
The correct answer is A.
Correct: A — Both reach the same final speed but Car X travels twice the distance of Car Y. Using v = at: X ends at 2.0×10 = 20 m/s; Y ends at 4.0×5.0 = 20 m/s, so final speeds match. Distance from rest under uniform acceleration is the area under the v–t graph (a triangle): s = 0.5×v×t. For X: 0.5×20×10 = 100 m; for Y: 0.5×20×5.0 = 50 m, so X goes twice as far. B — Wrong because equal final speeds do not imply equal distances; the longer acceleration time gives a larger area under the v–t graph. C — Wrong because the final speeds are equal (both 20 m/s), and distances are not the same (100 m vs 50 m). D — Wrong because while final speeds are equal, it is Car X, not Y, that travels twice the distance.