Suppose a 1000 kg car and an observer are both moving to the right at 20 m/s and 10 m/s, respectively. The driver steps on the gas, leading to acceleration equal to 5 m/s² (the moving observer maintains his velocity). The instantaneous rate of change of kinetic energy is equal to $mva$, the product of mass, velocity and acceleration. For an observer stationary with respect to the Earth, that rate of change is equal to $1000\times20\times5=10^5\space J/s$. For our moving observer, it is $1000\times10\times5=5\times 10^4\space J/s$. The difference can be accounted for by the static friction force at the interface between the tires and the road, which, for the moving observer, is acting upon a moving point, doing negative work on the car.
The same amount of fuel is being burned from the point of view of both observers. Let's suppose that to the stationary observer the entirety of the energy released by the combustion of the fuel goes into accelerating the car. To the moving observer, however, only half of it goes into accelerating the car, in agreement with the previous paragraph. The other half could be (could it?) be accounted for by the work done by the friction force against the moving road.
Here's my question: despite the math checking out, where is the measurable physical effect, from the point of view of the moving observer, of wherever the rest of that energy went to? Supposedly it's gone into the road, through the work done by the friction force. However, the road is clearly the same as it is for the stationary observer, so the moving observer wouldn't be able to detect any difference in its state through experiment (or could they?). What gives?
Thanks.
