Demonstration of a Principle:
    Conservation of Energy, or COE for short.
         Energy is not created or destroyed.  It just changes forms.

Demonstration:
 

Kinetic Energy	Potential Energy
The energy from speed.	The energy from height.

    To jump over a tall barrier requires a running start.
    Why?

Answer:
    When you jump, you convert the kinetic energy of forward speed into height.
    More speed, more height.

Reality Check:

The real world is a little more complicated.
Where does the energy go when you land and hold still?
It goes into heating your muscles, noise, waves in the floor and friction which heats the floor.  Just ask any ballerina how hot a shoe can get when it scuffs the floor tape.  That is conservation of energy at work, turning the kinetic energy of motion into heat.  That's why the brakes on your car stop you.  Motion gets turned into heat.  Brakes get very hot.   COE can account for friction but the math gets more complex.

Simple Conservation of Energy:

KE₁  + PE₁  = KE₂  + PE₂

1/2 m v²  = m g h