A particle is moving in a straight line. At time `t` the distance between the particle from its starting point is given by `x=t-6t^(2)+t^(3)`. Its acceleration will be zero at

Options

A. `t=1` unit time
B. `t=2` units time
C. `t=3` units time
D. `t=4` units time

Answer

B

Explanation

Given `x=t-6t^(2)+t^(3)`
On differentiating both sides w.r.t `x` two times, we get
`(dx)/(dt)=1-12t+3t^(2)`
`(d^(2)x)/(dt^(2))=-12+6t`
When acceleration `(d^(2)x)/(dt^(2)=0impliest=2` units time.