A particle is moving in a straight line such that its distance `s`at a – InterviewSolution

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1.	A particle is moving in a straight line such that its distance `s`at any time `t`is given by `s=(t^4)/4-2t^3+4t^2-7.`Find when its velocity is maximum and acceleration minimum.
Answer» `S=t^4/4-2t^3+4t^2-7` `V=(dS)/(dt)=t^3-6t^2+8t` `a=(dV)/(dt)=(d^2S)/(dt^2)=3t^2-12t+8=0` `t=(12pmsqrt(144-96))/6` `t=2pm2/sqrt3` `(d^2V)/(dt^2)=6t-12` `t=2+2/sqrt3` `(d^2V)/(dt^2)=6(2+2/sqrt3)-12` @` t=2-2/sqrt3`, V is minimum `(da)/(dt)=6t-12=0` `(d^2a)/(dt^2)=6>0` @`t=2` this willbe minimum.

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