A body at rest is moved along a horizontal straight line by a...

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to:

Options

A $t\dfrac{3}{2}$
B $t\dfrac{1}{2}$
C $t\dfrac{1}{4}$
D $t\dfrac{3}{4}$

Correct answer

A. $t\dfrac{3}{2}$

Step-by-step solution

$P =$ constant

$\dfrac{1}{2}m{v}^{2} = Pt$

$⇒ v ∝ \sqrt{t}$

$\dfrac{dx}{dt} = C\sqrt{t}$ $C =$ constant

by integration,

$x = C\dfrac{{t}^{\dfrac{1}{2} + 1}}{\dfrac{1}{2} + 1}$

$x ∝ {t}^{3 / 2}$

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