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AMU Medical AMU Solved Paper-2000

  • question_answer
    The motion of particle is described by the equation\[x=a+b{{t}^{2}}\]where a = 15 cm and \[\text{b}=\text{3 cm}/\text{sb }=\text{ 3 cm}/{{\text{s}}^{\text{2}}}.\]Its instant velocityat time 3 s will be

    A)  36 cm/s                              

    B)  9 cm/s

    C)  4.5 cm/s                             

    D)  18 cm/s

    Correct Answer: D

    Solution :

                     Velocity is defined as rate of change of displacement. \[\therefore \]  \[v=\frac{dx}{dt}\] Given,   \[x=a+b{{t}^{2}}\] Differentiating w.r.t. t, we get                 \[v=\frac{dx}{dt}=2\,bt\] Given,   b = 3 \[cm/{{s}^{2}}\],    t = 3 s. \[\therefore \]  \[v=2\times 3\times 3=18\,\,cm/s\]


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