A light inextensible string of length 5.28 m has particles A and B, of masses 0.25 kg and 0.75 kg respectively, attached to its ends. Another particle P, of mass 0.5 kg, is attached to the mid-point of the string. Two small smooth pulleys P₁ and P₂ are fixed at opposite ends of a rough horizontal table of length 4 m and height 1 m. The string passes over P₁ and P₂ with particle A held at rest vertically below P₁, the string taut and B hanging freely below P₂. Particle P is in contact with the table halfway between P₁ and P₂ (see diagram). The coefficient of friction between P and the table is 0.4. Particle A is released and the system starts to move with constant acceleration of magnitude a m s^-2. The tension in the part AP of the string is T_A N and the tension in the part PB of the string is T_B N.

1. Find T_A and T_B in terms of a.
2. Show by considering the motion of P that a = 2.
3. Find the speed of the particles immediately before B reaches the floor.
4. Find the deceleration of P immediately after B reaches the floor.