The hockey puck has a mass 0.16 kg. It starts from rest and reaches a speed of 22 m/s, during which the distance traveled is 1.2 m.
Initially the puck has no kinetic energy. After 1.2 m the kinetic energy is (1/2)*m*v^2 = .5*0.16*22^2 = 38.72. Let the net average force be F, the work done on the puck is F*d = F*1.2 = 38.72
=> F = 32.27 N
Another way of determining the force is to use the relation v^2 - u^2 = 2*a*s where s is the total distance traveled, u is the initial velocity, v is the final velocity and a is the acceleration.
22^2 = 2*a*1.2
=> a = 605/3
The force applied is 0.16*605/3 = 32.27 N