NEET Sample Paper NEET Sample Test Paper-16

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

    A) go on decreasing with time

    B) be independent of and \[\beta \]

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

    D) go on increasing with time

    Correct Answer: D

    Solution :

    \[x=a{{e}^{-\alpha t}}+b{{e}^{\beta t}}\] \[V=\frac{dx}{dt}=-a\alpha {{e}^{-\alpha t}}+b\beta {{e}^{\beta t}}\] Acceleration \[=A=\frac{dv}{dt}=a{{\alpha }^{2}}{{e}^{-\alpha t}}+b{{\beta }^{2}}{{e}^{\beta t}}\] As acceleration is positive so the value of the velocity will go on Increasing Hence, the correction option is (d).

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