The oil paradox

Level pending

We all know that the oil consumption by a car is almost proportional to its change in kinetic energy i.e. the more the velocity of a car, more is its oil consumption. Now consider this case. Car A

Car B

Two cars (Car \(A\) & Car \(B\)) are both moving with the same velocity in a straight road and both started at the same time. After some time Car \(A\) accelerates to a velocity double of the initial velocity.

Now according to ground observer the change in velocity of the Car \(A\) is =\(1/2m(2v)^2\) - \(1/2m(v)^2\) = \(3/2mv^2\) and according to a observer sitting in car \(B\) change in K.E. is \(1/2mv^2\)(as relative velocity between two cars is \(v\)) So with different changes of kinetic energy in two frames does it mean that oil consumption for two frames are different. Can you provide a possible explanation for your answer?

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