A particle is moving unidirectionally on a horizontal plane under the action of a constant power sup

Question

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement $(s)$ - time $(t)$ graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale)\

Professor PC Thomas Classes · Answer

(b) : Power supply $=$ constant\ so, $W=\frac{1}{2} m v^{2} ; P 	imes t=\frac{1}{2} m v^{2}$;\ $v=\sqrt{\frac{2 P}{m}} t^{1 / 2}$\ $S=\int_{0}^{t} v d t=\int_{0}^{t} \sqrt{\frac{2 P}{m}} t^{1 / 2} d t$\ $\Rightarrow S=\sqrt{\frac{2 P}{m}} \frac{2 t^{3 / 2}}{3}=\frac{2}{3} \sqrt{\frac{2 P}{m}} t^{3 / 2}$\ $S \propto t^{3 / 2}$\