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by casey2 4 hours ago
Mikes' answer is the most intuitive, but he rephrases the question in a possibly non intuitive way.

Odd that nobody mentioned power, which scales linearly with speed. Of course if you add linear increasing amounts of power to the system the energy will increase quadratically.

Power scaling linearly is more intuitive because doubling your speed requires twice the power to maintain the same force, why does it require twice the power? because you have half the time to power it.