A particle moves along a straight line such that its displacement any time t is given by: s=( #t^3 - 3t^2 +2#)m. The displacement when the acceleration becomes zero is?

#t^3 - 3t^2 +2#

1 Answer
A08
Jun 15, 2017

Displacement is given as
#s=( t^3−3t^2+2)# ......(1)

We know that Acceleration #a=(d^2s)/dt^2#
Differentiating (1) once with respect to #t# we get
#(ds)/dt=d/dt( t^3−3t^2+2)#
#=>(ds)/dt=3t^2−6t#

Differentiating once again we get
#(d^2s)/dt^2=d/dt(3t^2−6t)#
#(d^2s)/dt^2=6t−6#

Given condition is
#(d^2s)/dt^2=6t−6=0#
#=>t=1s#

From (1)
#s(1)=( 1^3−3xx1^2+2)#
#s(1)=0m#

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