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

Answer

B, C

Explanation

b,c. `v = (dx)/(dt) = -9 + t^2 = 0 rArr t = 3s `
The particle's velocity is getting zero at t = 3 s, where it changes
its direction of motion.
For 0lttlt3s, v is negative, a is positive, so particle is slowing
down.
For t gt 2, both v and a are positive, so the particle is speeding
up.