A particle moves in the xy-plane. Its coordinates are given as functions of time by x(t) = R (wt – sin wt) y(t) = R (1 – cos wt) where Rand", are constants.
(a) Sketch the trajectory of the particle. (This is the trajectory of a point on the rim of a wheel that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid.)
(b) Determine the velocity components and the acceleration components of the particle a! any time t.
(c) At which times is the particle momentarily a rest, what are the coordinates of the particle at these times? What are the magnitude and direction of the acceleration at these times?
(d) Does the magnitude of the acceleration depend on time? Compare to uniform circular motion.