Consider two particles A and B, of masses mA and mB, connected by a light inextensible string passing over a smooth fixed pulley and suppose that mA > mB .
As the particles move, one of them moves upwards in the same way as the other moves downwards, i.e.
the upward speed of B is equal to the downward speed of A,
the upward acceleration of B is equal to the downward acceleration of A,
the distance B moves up is equal to the distance A moves down.
The way in which each particle moves is determined by the forces which act on that particle alone, so to analyse the motion we consider the particles separately, i.e.