A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P . Its displacement in 4 s is 1 3 α 2 P m . The value of α will be ______

Question

A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P . Its displacement in 4 s is 1 3 α 2 P m . The value of α will be ______.

TestHub · Accepted Answer

Energy provided will be used to increase kinetic energy of the body. Therefore, 1 2 m V 2 = P t V = 2 P t m ⇒ d x d t = 2 P t m ⇒ ∫ 0 x d x = 2 P m ∫ 0 4 t 1 2 d t ⇒ x = 2 P m 2 3 t 3 2 0 4 ⇒ x = 16 P 3 = 1 3 × 16 P Hence, required value of α = 4 .

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