Newton's laws of motion — practice question

A light inextensible string, of length $5.28\text{ m}$, has particles $A$ and $B$ attached to its ends, with masses $0.25\text{ kg}$ and $0.75\text{ kg}$ respectively. A further particle $P$, of mass $0.5\text{ kg}$, is fixed at the string’s mid-point. Two smooth pulleys $P_1$ and $P_2$ are mounted at opposite ends of a rough horizontal table of length $4\text{ m}$ and height $1\text{ m}$. The string runs over $P_1$ and $P_2$, with particle $A$ kept at rest vertically under $P_1$, the string taut, and $B$ hanging freely below $P_2$. Particle $P$ is touching the table halfway between $P_1$ and $P_2$ (see diagram). The coefficient of friction between $P$ and the table is $0.4$. Particle $A$ is released and the system begins to move with constant acceleration of magnitude $a\,\text{m s}^{-2}$. The tension in the part $AP$ of the string is $T_A\text{ N}$ and the tension in the part $PB$ of the string is $T_B\text{ N}$.