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

  • question_answer
    If the distance ?s? metre traversed by a particle in t seconds is given by \[s={{t}^{3}}-3{{t}^{2}}\], then the velocity of the particle when the acceleration is zero, in metre/sec is [Karnataka CET 2004]

    A)            3

    B)            ? 2

    C)            ? 3

    D)            2

    Correct Answer: C

    Solution :

      Given  \[s={{t}^{3}}-3{{t}^{2}}\]                    \ \[v=\frac{ds}{dt}=3{{t}^{2}}-6t\],  \[a=\frac{{{d}^{2}}s}{d{{t}^{2}}}=6t-6\]                    Acceleration is zero, if \[6t-6=0\]Þ \[t=1\]                    \ Required velocity of particle at \[t=1\] is \[v=3{{(1)}^{2}}-6(1)\]                    \[\Rightarrow \,v=-3\].


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