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 ?

Options

A. Velocity is perpendicular to `vec v` and acceleration is directed anway from the origin.
B. Velocity and acceleration both are perpendicular to `vec r`
C. Velocity and acceleration both are parallel to `vec r`
D. Velocity is perpendicular to `vec r` and acceleration is directed towards the origin.

Explanation

`vec r = cos omega t hatx + sin omega t hat y `
`vec v = (d vec r)/(ct) = - omega sin omega t hat x + - omega cos omega t hat y`
`vec a = (d vec v)/(dt) = - omega^(2) cos omega hat x - omega ^(2) sin 2 omega t hat y`
` = -omega^(2) vec r`
- ve sign shows that acceleration is directed towards centre
`vec r . vec v = 0` i.e., position vector and velocity are perpendicular