A particle moves such that its position vector $\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\overrightarrow{\mathrm{v}}(\mathrm{t})$ and acceleration $\overrightarrow{\mathrm{a}}(\mathrm{t})$ of the particle
A particle moves such that its position vector $\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\overrightarrow{\mathrm{v}}(\mathrm{t})$ and acceleration $\overrightarrow{\mathrm{a}}(\mathrm{t})$ of the particle
- [JEE MAIN 2020]
- A
$\overrightarrow{\mathrm{v}}$ is perpendicular to $\overrightarrow{\mathrm{r}}$ and $\overrightarrow{\mathrm{a}}$ is directed towards the origin
- B
$\overrightarrow{\mathrm{v}}$ and $\overrightarrow{\mathrm{a}}$ both are parallel to $\overrightarrow{\mathrm{r}}$
- C
$\overrightarrow{\mathrm{v}}$ and $\overrightarrow{\mathrm{a}}$ both are perpendicular to $\overrightarrow{\mathrm{r}}$
- D
$\overrightarrow{\mathrm{v}}$ is perpendicular to $\overrightarrow{\mathrm{r}}$ and $\overrightarrow{\mathrm{a}}$ is directed away from the origin
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