A particle is moving along `x-`axis whose position is given by `x=4-9t+(t^(3))/(3)` then choose the CORRECT statement for thes motion`-`

Options

A. Direction of motion is not changing at any of the instants
B. For `0lttlt2s`, the particle is speeding up
C. Direction of motion is changing at `t=3`sec
D. For `0lttlt3s` the particle is speeding up.

Answer

C

Explanation

`x=4-9t+(t^(3))/(3)rArrv=(dx)/(dt)=(-9+t^(2))` and `a=((dv)/(dt))=2t`. Therefore (`vlt0` and `agt0` for `0lttlt3s`)