Oh, here's a question I've been wanting to hurt people with for awhile.
Let's say you're in a hybrid automobile at the top of a hill. Your vehicle can convert velocity now to velocity later at a given efficiency rate of A (that is, e.g., if you slow down 5m/s now, then later you can speed up by 5Am/s), with A of course being less than 1. You also have to deal with air resistance, which as usual goes up with the square of velocity. Let's say your drag constant (area * drag coefficient) is B (see
Drag Equation).
The question is, when driving down the hill, do you try to conserve as much kinetic energy as possible (i.e. don't use the brakes; just coast), despite increased losses due to air resistance? Or do you brake, losing some energy in the conversion process but also losing less due to air resistance?
Obviously a perfectly-efficient hybrid (A = 1) would go as slowly as possible on the hill, and a non-hybrid (A = 0) would go as fast as possible. It's in the middle where things get muddy.
