A block of mass 2 kg is pushed normally against a rough vertical wall with a force of 40 N, coefficient of static friction being 0.5. Another horizontal force of 15 N, is applied on the block in a direction parallel to the wall. With what minimum acceleration (in $m{s}^{-2}$) does the block move? (g=10 m/s²)

The force which may cause the tendency of motion or motion in the body is its own  weight and the applied horizontal force of 15N. The resultant of the forces 
F =  $\sqrt{{20}^2+{15}^2}=25N$
In a direction tan^-1  $\left(\frac{15}{20}\right)$= 37⁰ with the vertical.
 
The friction will, by its very virtue of opposing the tendency of relative motion will act in  a direction opposite to the resultant force.   Now, for the acceleration to be minimum,
the minimum force required = F – $\mu$N (as, $\mu$N is the maximum frictional force)
          = 25 – 0.5 x 40 = 5 N
$\therefore$ Minimum acceleration is  $\frac{5}{2}=2.5m/s^2$