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

  • question_answer
    If the path of a moving point is the curve \[x=at\], \[y=b\sin at\], then its acceleration at any instant       [SCRA 1996]

    A)            Is constant                            

    B)            Varies as the distance from the axis of x

    C)            Varies as the distance from the axis of y

    D)            Varies as the distance of the point from the origin

    Correct Answer: C

    Solution :

               \[\frac{dx}{dt}={{v}_{x}}=a\Rightarrow \frac{{{d}^{2}}x}{d{{t}^{2}}}=0={{a}_{x}}\]                    \[{{a}_{x}}\]is acceleration in x-axis                    \[\frac{{{d}^{2}}y}{d{{t}^{2}}}=-b{{a}^{2}}\sin at\Rightarrow {{a}_{y}}=-{{a}^{2}}y\]                    Hence, \[{{a}_{y}}\]changes as y changes.


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