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Lets say you need 600 HP seconds of energy to get your car to 60 MPH, assuming all the other loss sources (aero, RR, mechanical friction in drive train, etc) were eliminated, then your source of that 600 HP-sec would be most efficient at its best BSFC (without time as a constraint).
600 HP-secs for 1 sec
300 HP-secs for 2 sec
100 HP-secs fro 6 secs
I can't see any reason for that to become proportional, however that is mostly instinct on my part, and could be refuted easily with a logical counter explanation.
It is basically changing the inertial state of an object moving in a linear fashion. I do stumble on the exponential cost of accelerating a flywheel, but have seen that just running an engine with no load at different RPM seems to use a linear volume of fuel.
regards
Mech
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