Question

Which of the following graphs correctly represents a particle moving in a horizontal circle, if its magnitude of tangential acceleration is directly proportional to time and particle starts from rest?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given, $a_t\propto t$
or, $a_t=kt$, where $k$ is proportionality constant.
As we know that
$a_t=\frac{dv}{dt}=kt$
$\Rightarrow {\int }_0^{v}dv=k{\int }_0^{t}tdt\Rightarrow v=\frac{k{t}^2}{2}$

Hence, $v\propto t^2$ and $\text{at}t=0,v=0$
Also, as $t\to \infty ,v\to \infty$
Thus, the $v-t$ curve will be parabolic and increasing.