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

Power $P$ is given by $P=Fv$. Since $F=ma=m(dv/dt)$, we have $P=m(dv/dt)v$. Rearranging and integrating: $P{\int }_0^{t}dt=m{\int }_0^{v}vdv$.$$Pt=m\frac{v^2}{2}$$ $$v^2=\frac{2P}{m}t$$ Therefore, $v=\sqrt{\frac{2P}{m}}\cdot t^{1/2}$. This shows that $v\propto t^{1/2}$.