a particle moves in the xy plane such that at a time t it is at a point (x,y) where x=2cos(at) y=2sin(at) prove particle moves in a circular path with constant angular velocity. prove that the acceleration of the particle at time t is in the direction of the radius from the particle to the centre of its path. so i have R=[2cos(at),2sin(at)] V=[-2asin(at),2acos(at)] A=[-2a^2cos(at),-2a^2sin(at)] not sure how to show angular is constant. i can take |V| and that s constant but im not using angular velocity. for the second part: if if i take direction of A= (d2y/dt2)/(d2x/dt2)=tan(at) where d2y/dt2 is second derivative of y wrt t does this answer the question as motion is circle centre (o,0) so any radius will have tan (at) as its gradient?