If it takes 10 energy units to move a 10kg weight 10 meters, does the energy expended go up as the time used decreases?
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I’ve been thinking more about this, and I think I may have guess wrongly about what you meant. Here is a simple scenario where it would work like you think (energy is the same, even if one is faster):
Two space ships travel 100km. The first space ship accelerates to 100 m/s over the first km then travels the rest of the 99km at that speed with no more acceleration.
The second ship accelerates to 100 m/s over the entire 100km, not reaching it’s top speed until the very end of the journey.
In both cases the energy used is the same (the amount of kinetic energy the space ship has at 100 m/s), but the first ship would get to it’s destination much faster.
The key point that makes this work is that the top speed of each ship is the same – it’s only the acceleration that’s different.
So I guess the most correct answer to your original question is: it depends. A higher speed requires more energy, but it doesn’t matter how fast you reach that speed (ignoring real-life mechanical limitations).
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