-- If you are in motion, you must expend energy in an equal and opposite direction to return to a state of rest.--
Hmmm. In an electrically driven car, one gains energy through regenerative braking while slowing down to a rest.
That would require a very large fly-wheel. Where does the energy come from to spin it? Going down hill?
Do these cars have one?
Sorry for what might be a dumb question but I am no more versed on this technology than I am on voodoo.
When you move the electric car from rest, the chemical energy is transformed to electricity. The electricity drives electromagnets in the motor. The drive train converts the rotation of the motor into linear motion via the wheels. The moving vehicle now possesses kinetic energy and momentum. When you apply the "brakes", the linear motion of the car is transformed to rotation of the wheels. That rotation is fed back through the drive train to the motor where the back EMF can return a portion of the original electrical energy back to recharge the battery. You gain nothing. You do recover a small percentage of the original chemical energy. There is loss along the entire path of transformation each direction.
If you happen to be going downhill, the regenerative braking may transform some of your gravitation potential energy into chemical energy in the battery. Still, what goes up must come down. You'll have to climb that hill later and you'll burn more than you captured.