Question

A particle rotates in a circular path of radius $54m$ with varying speed $v=4t$${}^2$. Here $v$ is in m/s and $t$ in second. Find angle between velocity and acceleration at $t=3s$.

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

Answer: (C)

${45}^{\circ }$

$a_t=\frac{d}{dt}\left(4t^2\right)=8t,a_r=\frac{v^2}{R},\overrightarrow{a_{t=3}}=24\hat{r}+24\hat{\theta }\overrightarrow{v_{t=3}}=36\hat{\theta }$

Thus, angle between

$\overrightarrow{a_{t=3}}and\overrightarrow{v_{t=3}}is{45}^0$