A body is moving unidirectionally under the influence of a source of constant power. The square of its displacement in time t is proportional to

Step-by-step solution

By work-energy theorem, W = P × t = 1 2 m v 2 ⇒ v 2 = 2 P t m v = 2 P t m 1 / 2 or d s d t = 2 P t m 1 / 2 ∫ d s = ∫ 2 P t m 1 / 2 d t s = 2 P m 1 / 2 · 2 3 t 3 / 2 i.e. s ∝ t 3 / 2 s 2 ∝ t 3