Figure shows an arrangement  of a carriage system.  A force P is applied on the carriage B and moving rightward at 3 m/s² constant acceleration.  At the instant shown the velocity of B is 2 m/s.

(i) Determine the velocity of B relative to A.

(ii) Determine the acceleration of B relative to A

(iii) Determine the absolute velocity of C, Carriage A

(iv) Determine the absolute acceleration of carriage A

(v) Determine the force P and the tension in the rope if mass A= 50 kg and mass B=40 kg (neglect the masses of pulleys, rope and the friction forces at the wheels)