Question

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?
(a) Velocity and acceleration both are perpendicular to $\vec{r}$
(b) Velocity and acceleration both are parallel to $\vec{r}$
(c) Velocity is perpendicular to $\vec{r}$ and acceleration is
directed towards the origin
(d) Velocity is perpendicular to $\vec{r}$ and acceleration is
directed away from the origin

Answer 1

Answer:c

Explanation:

I am not writing the arrows and w =omega

r=coswtx+sinwty

v= -wsinwtx+wcoswty

a= -w^2coswtx+wsinwty= -w^2r

r.v=0 hence r is perpendicular to v

a is directed towards the origin