The position vector as a function of time of an object moving along a circular path is given by

hat$(r)(t)=3cos2ti+3sin2tj$

$2\mathrm{.}1$ Show that the objects' moves with a constant speed.

$2,2$ Show that the objects' position and velocity are perpendicular.

$2\mathrm{.}3$ Show that the force keeping the object in the circular path is directed lowards the eentre of the circular path.