A particle is moving along the x-axis whose position is given by ` x= 4 - 9t + t^3/3`. Mark the correct statement(s) in relation to its motion.

Options

A. direction of motion is not changing at any of the instant
B. direction of motion is not changing `t=3s`
C. for `0lttlt3`,s the particle is slowing down
D. for `0lttlt3`s, the particle is speeding up.

Answer

B, C

Explanation

The particle's velocity is getting zero at `t=3` s, where changes its direction of motion.
for `0lttlt3` s, V is negative, a is positive so particele is slowing down. For `tlt3`, both V and a are positive so the particle is speeding up.