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CMC Medical CMC-Medical VELLORE Solved Paper-2010

  • question_answer
    The displacement x of a particle varies with time \[t\]as \[x=a{{e}^{-\omega t}}+b{{e}^{\beta t}},\]where a, b, \[\alpha \] and \[\beta \] are positive constants. The velocity of the particle will

    A)  be independent of\[\alpha \]and\[\beta \]

    B)  go on increasing with time

    C)  drop to zero when\[\alpha =\beta \]

    D)  go on decreasing with time

    E)  None of the above

    Correct Answer: B

    Solution :

                    Velocity \[v=\frac{dx}{dt}=\frac{d}{dt}(a{{e}^{-\alpha t}}+b{{e}^{\beta t}})\]   \[=-a\alpha {{e}^{-\alpha t}}+b\beta {{e}^{\beta t}}\]


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