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Q.

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 4s is $\frac{1}{3} α^{2} \sqrt{P} m$ .The value of $α$ will be _______.

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answer is 4.

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Detailed Solution

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Power = FV = P = Constant
$\begin{array}{l} mav = P \Rightarrow av = \frac{p}{m} \Rightarrow vdv = \frac{p}{m} dt \\ \frac{v^{2}}{2} = \frac{p}{2} t \Rightarrow v = \sqrt{p} t^{1 / 2} \\ S = \sqrt{p} \cdot \frac{2}{3} {[t^{3 / 2}]}_{0}^{4} \Rightarrow S = \sqrt{p} \cdot \frac{1}{3} \cdot (4)^{2} \end{array}$

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