$A$ particle moves such that its position vector $\overrightarrow{r}(t) = \cos \omega t \hat{i} + \sin \omega t \hat{j}$,where $\omega$ is a constant and $t$ is time. Which of the following statements is true for the velocity $\overrightarrow{v}(t)$ and acceleration $\overrightarrow{a}(t)$ of the particle?

• A
  $\overrightarrow{v}$ is perpendicular to $\overrightarrow{r}$ and $\overrightarrow{a}$ is directed towards the origin.
• B
  $\overrightarrow{v}$ and $\overrightarrow{a}$ both are parallel to $\overrightarrow{r}$.
• C
  $\overrightarrow{v}$ and $\overrightarrow{a}$ both are perpendicular to $\overrightarrow{r}$.
• D
  $\overrightarrow{v}$ is perpendicular to $\overrightarrow{r}$ and $\overrightarrow{a}$ is directed away from the origin.