Question

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`

Answer 1

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`