Question

A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x$−axis. Identify all figures that correctly represent the motion qualitatively. ($a$=accelertaion, $v$=velocity, $d$=displacement, $t$=time)

• A. $\left(A\right)$
• B. $\left(B\right),\left(C\right)$
• C. $\left(A\right),\left(B\right),\left(C\right)$
• D. $\left(A\right),\left(B\right),\left(D\right)$

Answer 1

The correct option is D $\left(A\right),\left(B\right),\left(D\right)$

Given initial velocity $u=0$ and acceleration is constant.
So, it doesn’t change with time.

At time $t$, 1st equation of motion
$v=u+at$

As particle starts from rest $u=0$
$\therefore v=0+at\Rightarrow v=at$
$v\propto t$

From $3$rd equation of motion
$s=ut+\frac{1}{2}a{t}^2$

As particle starts from rest $u=0$
$s\propto t^2$

Final answer: (c).