If a particle moves according to the law s=6t2−t32 , then  the time at which it is momentarily at rest is

If a particle moves according to the law s=6t2t32 , then  the time at which it is momentarily at rest is

  1. A

    t=0 only

  2. B

    t=8 only 

  3. C

    t = 0, 8 

  4. D

    none of these   

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    Solution:

    We have ,

    s=6t2t32dsdt=12t3t22 and d2sdt2=123t

    When the particle is momentarily at rest, we have 

    dsdt=0 and d2sdt20 

    Now, 

    dsdt=0t=0,t=8

    Clearly, d2sdt20 for t=0,8 .

    Thus, the particle is momentarily at rest at t = 0, 8

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