Initial & Final Velocity on X-Axis: Why Equal?

[Aspekt]

As far as motion on the X-Axis, why typically are the initial velocity and final velocity values the same?

 

[lightgrav]

because the Force that causes acceleration (in projectile motion)
is the pull of Earth's gravity applied to the projectile.
This Force is Downward (by definition!) so the acceleration is, too.
So the other two acceleration components are zero.