A12-in.-radius cylinder of weight 16 lb rests on a 6-lb carriage. the system is at rest when a force p of magnitude 4 lb is applied. knowing that the cylinder rolls without sliding on the carriage and neglecting the mass of the wheels of the carriage, determine (a) the acceleration of the carriage, (b) the acceleration of point a, (c) the distance the cylinder has rolled with respect to the carriage after 0.5 s.