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CMC Medical CMC-Medical Ludhiana Solved Paper-2010

  • question_answer
    The position x of a particle varies with timer as \[x=a{{t}^{2}}-b{{t}^{3}}.\] The acceleration of the particle will be zero at time t equal to

    A)  \[\frac{2a}{3b}\]                                             

    B)  \[\frac{1}{b}\]

    C)  \[\frac{a}{3b}\]                                               

    D)  0

    Correct Answer: C

    Solution :

                    \[x=a{{t}^{2}}-b{{t}^{3}}\] Velocity \[v=\frac{dx}{dt}=2at-3b{{t}^{2}}\] Acceleration \[a=\frac{{{d}^{2}}x}{d{{t}^{2}}}=2a-6bt\] Substituting acceleration \[a=0\] \[\Rightarrow \]               \[2a-6bt=0\]                 \[t=\frac{2a}{6b}=\frac{a}{3b}\]


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