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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 so that its velocity at any point is given by \[{{v}^{2}}=a+bx\], where \[a,b\ne 0\]are constants. The acceleration is [MP PET 1989]

    A)            Zero

    B)            Uniform

    C)            Non-uniform

    D)            Indeterminate

    Correct Answer: B

    Solution :

               \[{{v}^{2}}=a+bx\] Þ \[2v\frac{dv}{dt}=b\frac{dx}{dt}\]Þ\[2v\frac{dv}{dt}=bv\] Þ \[\frac{dv}{dt}=\frac{b}{2}\]                    Hence acceleration is constant or uniform.


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