JIPMER Jipmer Medical Solved Paper-2000

  • question_answer
    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)  \[{{t}^{3/2}}\]                  

    C)  \[{{t}^{2}}\]                      

    D)         \[{{t}^{3/4}}\]

    Correct Answer: B

    Solution :

    As power\[=F\times \upsilon =m\frac{dv}{dt}\times v=\]constant k \[\upsilon d\upsilon =\frac{k}{m}dt\]                                     ?(i) Now integrating equation (i), we get \[{{\upsilon }^{2}}=\frac{2kt}{m}\] or            \[\upsilon =\frac{dx}{dt}=\sqrt{\frac{2k}{m}}{{t}^{1/2}}\] hence   \[x\propto {{t}^{3/2}}\]


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