A particle moves so that its position vector varies with time as $\overrightarrow{r}=A\cos \omega t\hat{i}+A\sin \omega t\hat{j}$. The initial velocity of the particle is

The correct option is A $A\omega \hat{j}$
Given,
$\overrightarrow{r}=(A\cos \omega t\hat{i}+A\sin \omega t\hat{j})$
$\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}$
Substituting $\overrightarrow{r}$ in the above equation, we have
$\overrightarrow{v}=A\frac{d}{dt}\left(\cos \omega t\right)\hat{i}+A\frac{d}{dt}\left(\sin \omega t\right)\hat{j}$
$=-A\omega \cos \omega t\hat{i}+A\omega \sin \omega t\hat{j}$
At $t=0,$
$v=-A\omega \sin 0\hat{i}+A\omega \cos 0\hat{j}=A\omega t\hat{j}$
Final Answer: (B)