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

  • question_answer
    A particle is moving in a straight line. Its displacement at time t is given by \[s=-4{{t}^{2}}+2t\], then its velocity and acceleration at time \[t=\frac{1}{2}\] second are                 [AISSE 1981]

    A)            ? 2, ? 8

    B)            2, 6

    C)            ? 2, 8

    D)            2, 8

    Correct Answer: A

    Solution :

               Displacements \[s=-4{{t}^{2}}+2t\]                    Now velocity \[v=-8t+2\] and its acceleration \[a=-8\]                    So \[{{\left( \frac{ds}{dt} \right)}_{t=1/2}}=-8\times \frac{1}{2}+2=-2\]and \[{{\left( \frac{{{d}^{2}}s}{d{{t}^{2}}} \right)}_{t=1/2}}=-8\].


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