You Can see in this arrangement if block A moves a distance x, then block B moves a distance x/2.
Velocity of A, v=dx/dt
Velocity of B = d(x/2)/dt =½dx/dt =v/2
Similarly acceleration of A, a=dv/dt
and acceleration of B =d(v/2)/dt =½dv/dt=a/2
So the acceleration of block B is half that of A. Of course, its direction is opposite. But one can always change directions in such systems adding extra pulleys.
