Question

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

• A. The direction of motion is not changing at any of the instance
• B. The direction of motion is changing at $t=3s$
• C. For $0<t<3s$, the particle is slowing down
• D. $0<t<3s$, the particle is speeding up

Answer 1

Answer: (B), (C)

The correct options are
B The direction of motion is changing at $t=3s$
C For $0<t<3s$, the particle is slowing down

$B,C$

$x=4-9t+\frac{t^3}{3}$

$V=\frac{dx}{dt}=-9+t^2$

$V=0\Rightarrow 0=-9+t^2$

$\Rightarrow t=3s$

$\therefore$ It's direction of motion changes at $t=3s$.

The body have an initial velocity and it becomes $O$ at $t=3s$, during this period, the particle $B$ slowing down.