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 sec is The value of will be ________ . [2023]

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Solution

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 4 sec is $\frac{1}{3} α^{2} \sqrt{P} m .$ The value of $α$ will be ________ . [2023]

Ans.
(4)

$\frac{1}{2} m v^{2} = P t$

$v = \sqrt{\frac{2 P t}{m}}$

$\frac{d x}{d t} = \sqrt{\frac{2 P t}{m}}$

$x = \sqrt{\frac{2 P}{m}} \frac{2}{3} {[t^{3 / 2}]}_{0}^{4}$

$x = \frac{16 \sqrt{P}}{3}$ $= \frac{1}{3} \times 16 \sqrt{P}$

$\Rightarrow α = 4$

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