A body is moved along a straight line by a machine delivering constant power. The distance traversed by the body in time t is proportional to

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$t^{\frac{1}{2}}$

$t^{\frac{3}{4}}$

$t^{\frac{3}{2}}$

$t^{2}$

answer is C.

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Detailed Solution

$\begin{array}{l} P = F υ = \frac{m d υ}{d t} υ \Rightarrow m υ d υ = P d t \\ \Rightarrow \frac{m υ^{2}}{2} = P t \Rightarrow υ \frac{d x}{d t} = \sqrt{\frac{2 P t}{m}} \Rightarrow d x = \sqrt{\frac{2 P}{m}} t^{\frac{1}{2}} d t \Rightarrow \end{array}$

on integration $x = \frac{2}{3} \sqrt{\frac{2 P}{m}} t^{\frac{3}{2}}$

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