Physics - W.E.P. Question with Solution | TestHub

Here, $P=$ constant, or, $\frac{\Delta W}{\Delta t}=P$ $\Delta W=P\Delta t$ or, $W=Pt$ or $\frac{1}{2}m{v}^2=Pt$ [Using work-energy theorem] or $v^2=\frac{2P}{m}t$ or $v=\sqrt{\frac{2P}{m}}{t}^{1/2}$ or $dx=\sqrt{\frac{2P}{m}}{t}^{1/2}dt$ Integrating both sides, ${\int }_0^{x}dx=\sqrt{\frac{2P}{m}}{\int }_0^t{t}^{1/2}dt$ $$\begin{array}{rl}& x=\sqrt{\frac{2P}{m}}\left(\frac{2}{3}\right)t^{3/2}\\ & \therefore x\propto t^{3/2}\\ & \text{ or displacement }\propto (\text{ time }{)}^{3/2}\end{array}$$