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.