What does it mean to say that in any system the total energy score stays the same?
It's one of the fundamental rules in physics that energy can't be created or destroyed. Relativity says matter and energy can be traded, but most of the time that is irrelevant.
Energy can change form. So you might have chemical energy in the fuel for your car, and some of that is converted to kinetic energy (energy of motion) when you drive. And then when you use the brakes, that energy is changed into heat energy (the brakes get hot). The total amount of energy stays the same though.
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