• # question_answer 45) A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to-                             A) ${{t}^{1/2}}$                        B) ${{t}^{3/4}}$C) ${{t}^{3/2}}$                                    D) ${{t}^{2}}$

$\text{P}=\text{Fv}=mav=m\left( \frac{dv}{dt} \right)\text{ }v\text{ }\Rightarrow \frac{P}{m}\text{dt}=v\text{ }dv$ Now $\Rightarrow \,\,\,\frac{P}{m}\,\times \,t=\frac{{{v}^{2}}}{2}\,\,\Rightarrow \,\,v={{\left( \frac{2P}{m} \right)}^{1/2}}\,\,({{t}^{1/2}})$ $\therefore \,\,s={{\left( \frac{2P}{m} \right)}^{1/2}}\,\,\left[ \frac{2{{t}^{3/2}}}{3} \right]\,\,\,\Rightarrow \,\,s\propto \,\,{{t}^{3/2}}$