Atennis ball, 0.314 kg, is accelerated at a rate of 164 m/s2 when hit by a professional tennis player. what force does the player's tennis racket exert on the ball?

Newton's 2nd law of motion:

                    Force = (mass) x (acceleration)

                             = (0.314 kg) x (164 m/s²)

                             =    51.5 newtons

                         (about 11.6 pounds) .

Notice that the ball is only accelerating while it's in contact with the racket.
The instant the ball loses contact with the racket, it stops accelerating, and
sails off in a straight line at whatever speed it had when it left the strings.