Describe how the horizontal position of The baseball varies overtime is the change in position constant variable? Why might this be so?

When you hit a baseball with a bat, you are applying a force only in the time while the bat is in contact with the ball, after that, the horizontal speed of the ball is constant. (if you ignore the friction of the air)

This happens because of the second Newton's law:

Force is equal to mass times the acceleration or:

F = m*a

If we do not have a force, then we do not have acceleration.

This means that the change in position for a fixed amount of time is constant, so horizontal speed is constant.