Alternative Viewpoint

Constant acceleration equation along y:   vy2 = voy2 + 2ay Δy

Multiply by m/2:    ½ m vy2 = ½ m voy2 + may Δy

Example: a ball thrown straight up from y=0 and reaches y=h before falling back to y=0.

At top, final velocity is zero. We get:  0 = ½ m voy2 - mgh   or   mgh = ½ m voy2

Going down, the initial velocity that is zero, so:  ½ m vy2 = mgh

Obvious conclusion:  Final velocity equals the initial velocity.

Something new:   The kinetic energy decreases on the way up, and increases back to the original amount on the way down. The kinetic energy is transformed into gravitational potential energy   U = mgh.

Kinetic energy is energy associated with motion.
Potential energy is energy associated with position.