4. Particle kinematics: circular motion A particle P moves with constant speed u anticlockwise around a circle of radius b with centre O in the (x, y)-plane. At time t = 0, P is at the point (b, 0). (a) Explain why the position of the particle at time t is given by r(t) = bcos(ut/b) i + bsin(ut/b) j, where i and j are unit vectors in the x and y directions, respec- tively. (b) Find the velocity and acceleration vectors of the particle. (c) Show that r = -war, where w = u/b. (d) Show that the velocity in a plane polar coordinate system centred at the origin O is given by r = u0, (2) where O is a unit vector in the direction of increasing 0. (e) By differentiating (2) find the acceleration of P in polar coordi- nates and show that it is equivalent to the Cartesian form found in part (b)