A particle moves such that its position vector `vecr (t) = cos omegahati + sin omegat hatj` where `omega` is a constant and t is time . Then which of the following statements is ture for the velocity `vecv` (t) and acceleration `veca` (t) fo the particle:

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)`