A.10 kg hockey puck is at rest. it encounters a force of 20 n for 0.2 seconds that sets it in motion. over the next 2 seconds it encounters 0.4 newton’s of resistance force. finally it encounters a final force of 24 n for 0.05 seconds in the direction of motion. what is the final velocity of the hockey puck? ?

The mechanical impulse, of a force, is a vectorial magnitude that relates this force to the duration of its performance.
 We have then:
 I = F * delta t.
 Since the impulse is a vector, we can then calculate the vector sum as:
 I = ((20) * (0.2)) - ((0.4) * (2)) + ((24) * (0.05))
 I = 4.4 N.s
 Then, by definition:
 I = delta p
 I = delta m * v
 I = m * delta v
 I = m * (v-0)
 Clearing v:
 v = I / m
 v = (4.4) / (0.10)
 v = 44 m / s
 
 the final velocity of the hockey puck is
 v = 44 m / s