Assume a truck of mass 1 ton braking from 60mph to 0 on a road surface.
From the reference frame of the road, the following energy is transferred to the brakes: 1 ton * 60mph^2 / 2 = 1800 ton mph.
From the reference frame of the truck, the following energy is transferred to the brakes: 1 ton * 60mph^2 / 2 = 1800 ton mph. The curve is different but that doesn't seem to matter.
But from the reference frame traveling at 30mph we get something different. Here we must consider the braking in 2 segments due to a sign problem: 1 ton * 30mph^2 / 2 + 1 ton * (-30mph)^ 2 / 2 = 900 ton mph.
Back to the first case, if we consider it in two segments we get this: 1 ton * 60mph^2 / 2 - 1 ton * 30mph^2 / 2 + 1 ton * 30mph^2 / 2 = 1 ton * 60mph^2 / 2 = 1800 ton mph.
Yes, I know ton mph is a strange energy unit. The problem is easier to understand without any unit conversions at all in it.
The problem seems to have something to do with picking unnatural reference frames, but defining natural reference frame resists. Normally I am accustomed to solving this problem in momentum only and always get the right result, but that doesn't apply right to friction heating. The explanation of kinetic energy transfer into the fuel doesn't work in this specific scenario.
The term for what I am looking for is the frame invariant calculation. The kinetic energy should indeed be different, but the energy added to the brakes should always be the same.