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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Application in Mechanics and Rate Measurer

  • question_answer
    A particle moves in a straight line in such a way that its velocity at any point is given by \[{{v}^{2}}=2-3x\], where x is measured from a fixed point. The acceleration is                                                               [MP PET 1992]

    A)            Uniform

    B)            Zero

    C)            Non-uniform

    D)            Indeterminate

    Correct Answer: A

    Solution :

               Velocity, \[{{v}^{2}}=2-3x\]            Differentiating with respect to t, we get            \[2v\frac{dv}{dt}=-3.\frac{dx}{dt}\] Þ\[2v\frac{dv}{dt}=-3v\]Þ\[\frac{dv}{dt}=-\frac{3}{2}\]            Hence acceleration is uniform.


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