NEET Sample Paper NEET Sample Test Paper-51

  • 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) \[{{t}^{2}}\]

    Correct Answer: C

    Solution :

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

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