Question

A particle is moving on a circular track of radius 4 m such that its tangential acceleration is 2t m/$s^2$. If the particle starts from rest, then at what time the angle between velocity and acceleration will be ${45}^{\circ }$?

• A. 5 sec
• B. 4 sec
• C. 3 sec
• D. 2 sec

Answer 1

The correct option is D 2 sec

For $\theta ={45}^{\circ }$ between $\overrightarrow{a}$ and $\overrightarrow{v}$
$a_t=a_c\Rightarrow a_t=\frac{dv}{dt}\Rightarrow {\int }_0^{v}dv={\int }_0^{t}2tdt$
$v=t^2\Rightarrow a_c=\frac{v^2}{R}=\frac{t^4}{4}$
$a_t=a_c\Rightarrow 2t=\frac{t^4}{4}\Rightarrow t=2sec$