Question

A particle moving along $x-$axis whose position is given by $x=4-9t+\frac{t^3}{3}$ then choose the correct statement(s) for this motion-

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

Answer 1

Answer: (B), (C)

For $0<t<3s$, the particle is slowing down
Direction of motion is changing at $t=3sec$

$x=4-9t+\frac{t^3}{3}\Rightarrow v=\frac{dx}{dt}=(-9+t^2)$ and $a=\left(\frac{dv}{dt}\right)=2t$ . Therefore ($v<0$)

For period $0<t<3s$ $\Rightarrow \overrightarrow{a}.\overrightarrow{v}$ $<0$ for period $0<t<3s$