# The oil paradox

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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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