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A particle moves so that its position vector is given by $\vec{r} = \cos \omega t\hat{x} + \sin \omega t\hat{y}$. Where $\omega$ is a constant. Which of the following is true?
Explanation
Given: Position vector $\vec{r} = \cos \omega t\hat{x} + \sin \omega t\hat{y}$ $\therefore$ Velocity, $\vec{v} = -\omega \sin \omega t\hat{x} + \omega \cos \omega t\hat{y}$ and acceleration, $\vec{a} = -\omega^{2}\cos \omega t\hat{x} - \omega^{2}\sin \omega t\hat{y} = -\omega^{2}\vec{r}$ $\vec{r} \cdot \vec{v} = 0$ hence $\vec{r} \perp \vec{v}$ and $\vec{a}$ is directed towards the origin.