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  4. A particle moves along a straight line such that its displacement at any time t is given by s=t3-3t2+2m. The displacement when the acceleration becomes zero is:

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Q. A particle moves along a straight line such that its displacement at any time t is given by $ s=t^{3}-3t^{2}+2m. $ The displacement when the acceleration becomes zero is:

Jharkhand CECEJharkhand CECE 2002

Solution:

Acceleration is equal to rate of change of velocity. Given,
$s=t^{3}-3 t^{2}+2$
Velocity $ v=\frac{d s}{d t}=3 t^{2}-6 t$
Acceleration $ a=\frac{d^{2} s}{d t^{2}}=\frac{d v}{d t}=6 t-6 $
At $ a=0,$ we have $ 6 t-6=0$
$\Rightarrow t=1 \,s $
Hence, $s=(1)^{3}-3(1)^{2}+2$
$=1-3+2=0$