Question

A particle starts from origin $\text{O}$ from rest and moves with a uniform acceleration along the positive $x-$axis. Identify all figures that correctly represent the motion quantitatively.
($a=$ acceleration, $v=$ velocity, $x=$ displacement, $t=$ time)

• A. $\text{(A),(B), (C)}$
• B. $\text{(A)}$
• C. $\text{(A), (B), (D)}$
• D. $\text{(B),(C)}$

Answer 1

The correct option is C $\text{(A), (B), (D)}$

Given,

initial velocity, $u=0$ and

acceleration, $a=\text{constant}$

So, graph $\left(\text{A}\right)$ is correct.

At time $t$, using equations of motion

$v=0+at$

$\Rightarrow v=at....\left(1\right)$

Also,

$x=0\left(t\right)+\frac{1}{2}a{t}^2$

$\Rightarrow x=\frac{1}{2}a{t}^2....\left(2\right)$

Using equations $\left(1\right)$ and $\left(2\right)$ we get the graphs $\text{(A), (B) and (D)}$.


Hence, $\left(\text{C}\right)$ is the correct answer.