(A) Show that the position of a particle on a circle of radius R with center at the origin (x=0,y=0) is given in unit vectors by r=cosθi+sinθj, where θ is the angle of the position vector with the x axis.

B) If the particle moves with constant speed v and period T, starting on the x axis at t=0, find an expression for θ in terms of the time and T.

C) Differentiate the position vector twice with respect to time to find the acceleration and show that it is the centripetal acceleration, whose magnitude is given by equation (a=(v^2)/r) and whose direction is toward the center of the circle. (Not that the unit vectors i and j are constants, independent of time.)