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

  • question_answer
    The position of a point in time ?t? is given by \[x=a+bt-c{{t}^{2}}\], \[y=at+b{{t}^{2}}\]. Its acceleration at time ?t? is   [MP PET 2003]

    A)            \[b-c\]

    B)            \[b+c\]

    C)            \[2b-2c\]

    D)            \[2\sqrt{{{b}^{2}}+{{c}^{2}}}\]

    Correct Answer: D

    Solution :

               Acceleration in direction of x-axis = \[\frac{{{d}^{2}}x}{d{{t}^{2}}}=-2c\]  and acceleration in direction of y-axis  = \[\frac{{{d}^{2}}y}{d{{t}^{2}}}=2b\]                    Resultant acceleration is                    =\[\sqrt{{{(-2c)}^{2}}+{{(2b)}^{2}}}=2\sqrt{{{b}^{2}}+{{c}^{2}}}\]


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