A partile is moving along `x-`axis such that its position is given by `x = 4 - 9t + (t^(3))/(3)` where `t` is time in seconds, `x` is in meters, Mark the correct statement(s) :

Options

A. Direction of motion is not changing at any of the instants
B. Direction of the motion is changing at `t = 3` seconds
C. For `0 lt t lt 3` sec. the particle slowing down
D. For `3 lt t lt 6` sec. The particle is speeding up

Answer

B, C, D

Explanation

`v = (dx)/(dt) = 0 - 9 + (3t^(2))/(3)`
`{:(v=0,"at" t= 3),("Also",a=2t):}`
The particle's velocity will be zero at `t = 3` sec. where it changes its direction of motion. For `0 lt t lt 3` sec. `v` is `-ve` and `a` is `+ve` so particle is slowing down.