Maximum acceleration of block A after its collision with block B has magnitude (assume the collision to be elastic)

 

As the blocks have same mass and collision is elastic, their velocities are exchanged after collision.

After collision, velocity of block A is v. Also, at maximum compression of the spring, velocity of block A is zero.

Thus, by conservation of energy $\frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$

$x=$ max. compression $=\sqrt{\frac{m}{k}}V$

Max acceleration of block A is $\frac{kx}{m}=\frac{k\left(\sqrt{\frac{m}{k}}V\right)}{m}=\sqrt{\frac{k}{m}}V$