The 1.2 kg ball is accelerated from rest to a speed of 6.5 m/s. Momentum is given as the product of mass and velocity. Initially as the ball was at rest the momentum was 0. When it is moving at 6.5 m/s the momentum is 1.2*6.5 = 7.8 kg*m/s. The change in momentum is 7.8 kg*m/s
The impulse that leads to the change in velocity of the ball is 7.8 kg*m/s
If a constant force of 39 N acting on the ball results in the change in its velocity, the product of the time for which it acts and the force itself is equal to the impulse. Or 7.8 = 39*t, t = 7.8/39 = 0.2 s
The force acting for 0.2 s increases changes the velocity of the ball from 0 to 6.5 m/s.