For a spring with a spring constant k, the potential energy stored when it is compressed or elongated such that the length of the spring changes from its equilibrium length by x, is given as (1/2)k*x^2
Here, the potential energy stored when the spring is compressed is (1/2)*4*4/100 = 2/625 N.
If the spring is released and it pushes a puck, the potential energy in the spring in converted to the kinetic energy of the puck. For a puck weighing m kg, and traveling with a velocity v, the kinetic energy is (1/2)*m*v^2
Here, the puck weighs 100 g. When the energy of 2/625 N is converted to the kinetic energy of the puck and its velocity is v, we get 2/625 = (1/2)*0.1*v^2
=> v^2 = (2/625)*2/0.1
=> v = 0.2529 m/s
The required velocity of the puck is 0.2529 m/s.