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 vector is parallel to position vector
B. Velocity vector is perpendicular to position vector
C. Acceleration vector is directed towards the origin
D. Acceleration vector is directed away from the origin

Answer

B, C

Explanation

`vec(r)=a cos omegat hat(i) + a sin omega t hat(j)`
velocity `=vec(v)=(dvec(r))/(dt)=-a omega sin omega t hat(i)+a omega cos omega t hat(j)`
Acceleration `=(d^(2)vec(r))/(dt^(2))=-a omega^(2) cos omegat hat(i)-a omega^(2) sin omega t hat(j)=-omega^(2)vec(r)`