question_answer

A particle moves so that its position vector is given by \[\vec{r}=\cos \omega t\text{ }\,\hat{x}+\sin \omega t\text{ }\hat{y}\]. Where \[\omega \] is a constant.  Which of the following is true? [NEET - 2016]

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

Correct Answer: C

Solution :

[c]

hence

is directed towards the origin.