A body is moving unidirectionally under the influence of a source&...

By work-energy theorem,

$W = P \times t = \dfrac{1}{2}mv^{2}$

$⇒ v^{2} = 2\dfrac{Pt}{m}$

$v = \left(\dfrac{2Pt}{m}\right)^{1} / 2$

or $\dfrac{ds}{dt} = \left(\dfrac{2Pt}{m}\right)^{1} / 2$

$∫ ds = ∫ \left(\dfrac{2Pt}{m}\right)^{1} / 2dt$

$s = \left(\dfrac{2P}{m}\right)^{1} / 2 \cdot \dfrac{2}{3}t^{3 / 2}$

i.e. $s ∝ t^{3 / 2}$

$s^{2} ∝ t^{3}$