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

$\text{ Substituting }\overrightarrow{r}=(A\cos \omega t\widehat{i}+A\sin \omega t\widehat{j})\text{ in }\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}\text{ we have }$

$\begin{array}{l}\overrightarrow{v}=A\frac{d}{dt}(\cos \omega t)\widehat{i}+A\frac{d}{dt}(\sin \omega t)\widehat{j}\\ =-A\omega \sin \omega t\widehat{i}+A\omega \cos \omega t\widehat{j}\\ \text{ At }t=0,v=-A\omega \sin 0\widehat{i}+A\omega \cos 0\widehat{j}=A\omega \widehat{j}\end{array}$