- #1

snoopies622

- 791

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I have a battery-powered toy car. I turn it on and it accelerates from speed 0 to speed 1. (I'm leaving out units for simplicity here.) Since kinetic energy is a function of the square of an object's speed, the change in the car's kinetic energy is [itex] 1^2 - 0^2 = 1 - 0 = 1 [/itex]. All this energy comes from the battery.

Now look at this event from the reference frame of someone who is initially ahead of the car and walking towards it at speed 3. To him, the car accelerates from speed 3 to speed 4, and the change in kinetic energy is therefore [itex] 4^2 - 3^2 = 16 - 9 = 7 [/itex]. Again, all this energy comes from the battery.

How can a battery give up 1 unit of energy in one frame and 7 units in another frame? What if it was built with only 5 energy units in the first place?