Question

A tennis ball traveling at 12m/s was approaching the tennis players racket. The ball was hit back with a speed of 38m/s in the opposite direction from where it came

Answer 1

I assume the question is about the change of ball's velocity.

The initial velocity of the ball is

$$v_i = 12m/s$$

The final velocity is

$$v_f = -38m/s$$

It is negative, since its direction is opposite to the initial one. Thus, the change of the velocity is the following:

$$\Delta v = v_f-v_i = -38m/s-12m/s = -50m/s$$

Answer. $-50m/s$.