The forces acting on the block A at any given moment are the gravity force which is equal to 300N down, and the weight of the block B ("transmitted" via the cord and the pulleys) up (50N).
The net force F is constant (300-50=250N) and acts downward. It gives the block the constant acceleration of F/m by Newton's second law. m is the mass of the block A and it is equal to its weight 300N divided by g (the gravity acceleration).
Therefore the speed will be (F/m)*t (t is for time).
The equation for t is
[F/(300/g)]*t = 2.5,
so t=2.5*300/(250*9.8)= approx. 0.306(s). The distance travelled by the block A (or the block B) will be (g*t^2)/2= approx. 0.459(m).