edit: this problem is about energy discrepancies when changing frames and is no homework. suppose I accelerate a car from 0 to 100. the energy difference is 1/2 m v^2 - 0 = 1/2 m 100^2 = 5000 m joules now I accelerate another car from 0 to 50. the energy difference is 1/2 m v^2 - 0 = 1250 m joules when this car reaches 50, I change the frame to the frame in which the car is in rest. In this new frame, I again accelarate to 50. The energy change is again 1250 m joules Now I change back the frame to the starting frame. Both cars reached a 100, but the second one seems to have done it with half the energy. Where did I make the mistake? I honestly don't know, if anyone could help it would be very much appreciated.