A soccer player kicks a soccer ball of mass 0.40 kg that is initially at rest. The player's foot is in contact with the ball for 2.0 multiplied by 10-3 s, and the force of the kick is given by
F(t) = [(7.2 multiplied by 106)t - (3.0 multiplied by 109)t2] N,
for 0 t 2.0 multiplied by 10-3 s, where t is in seconds. Find the magnitudes of the following:
(b) the average force exerted by the player's foot on the ball during the period of contact,
(c) the maximum force exerted by the player's foot on the ball during the period of contact, and
(d) the ball's velocity immediately after it loses contact with the player's foot.