Question

A particle moves along $X-$ axis. It's equation of motion is $x=2t(t-2)$ where $t$ is in $\text{seconds}$. Choose the correct statement(s).

• A. The particle moves with a non-uniform acceleration.
• B. The particle momentarily comes to rest at $t=1\text{sec}$.
• C. The particle performs $\text{SHM}$
• D. The given equation represents uniformly accelerated motion for $t>1\text{sec}$

Answer 1

Answer: (B), (D)

The given equation represents uniformly accelerated motion for $t>1\text{sec}$

At $t=0$, the particle is at the origin$(x=0)$

Velocity of the particle is given by,

$V=\frac{dx}{dt}=4t-4.$

For the particle to come at rest, $V=0$

$\Rightarrow 4t-4=0$

$t=1\text{sec}$

Hence, it comes to rest momentarily at $t=1\text{sec}$.

After $t=1\text{sec}$, the particle will reverse it's direction of motion and move with uniform acceleration $a=\frac{dv}{dt}=4{\text{m/s}}^2$ towards the positive $X-$ axis.

As the acceleration is constant throughout the motion of the particle, it cannot execute $\text{SHM}$.

Hence, option $\left(B\right)$ and $\left(D\right)$ are the correct choices.