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BHU PMT BHU PMT (Mains) Solved Paper-2011

  • question_answer
    The displacement\[x\]of a body varies with time as \[x=-\frac{1}{3}{{t}^{2}}+16t+3\] where\[x\]is in metre and t in second. The time taken by the body to come to rest is

    A)  12s                                       

    B)  24s

    C)  30s                                       

    D)  36s

    Correct Answer: B

    Solution :

                      \[x=-\frac{1}{3}{{t}^{2}}+16t+3\] Velocity,              \[v=\frac{dx}{dt}\]                                 \[=\frac{d}{dt}\left( -\frac{1}{3}{{t}^{2}}+16t+3 \right)\]                                 \[=-\frac{2}{3}t+16\] The body comes to rest, so\[v=0\] i.e.,        \[-\frac{2}{3}t+16=0\] \[\Rightarrow \]               \[\frac{2}{3}t=16\]                 \[t=\frac{16\times 3}{2}\]                 \[=24\,s\]


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