A 9 in radius cylinder of weight 18lb rests on a 6lb carriage. the system is at rest when a force p of magnitude 2.5lb is applied as shown for 1.2s. (p comes out of the cart that the cylinder is sitting on) knowing that the cylinder rolls without sliding on the carriage and neglecting the mass of the wheels of the carriage, determine the resulting velocity of (a) the carriage, (b) the center of the cylinder.