Question

A body starts from rest and moves with a constant acceleration. Which one of the following graphs represent the variation of its kinetic energy $K$ with the distance travelled $x$ ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

As mentioned in question, body is moving with constant acceleration, so

$a=\text{constant}$

Now apply the third equation of motion,

$v^2=u^2+2as$

Here, $u=0\&s=x$

$\therefore v^2=2ax$

And we know that, kinetic energy of body is given by

$K=\frac{1}{2}m{v}^2=\frac{1}{2}m\times 2ax=max$

In the above equation, $m$ and $a$ are constants. Also, it's a first degree equation of $K$ and $x$.

Therefore, the graph of $K\text{vs}x$ will be stright line passing through origin ( it will pass through origin as $u=0$).

So, option $\left(C\right)$ is correct.