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So I saw this physics website that said drag grows quadratically with speed. Meaning the drag force at 200 km/h is 4 times what it is at 100 km/h. Ok I'm fine with that. But then it said the work required to accelerate to that speed grows cubically. Meaning I need 8 times the power to accelerate from 100 km/h to 200km/h? this part I dont get. So if my imaginary engine was producing x kilowatts or kilonewtons, and I pressed a button and its now doing 4x:

  • Isnt it logical that I should accelerate if I am going only 100 km/h, since drag isnt 4x yet??
  • Shouldnt I keep accelerating until equilibrium out at 200 km/h?

Update: the power vs force distinction solves it. I was mislead by the use of the word "accelerate" in that page. I thought it was discussion about drag and acceleration. There is no accelerate. The power required to go from A to B in half the time is 2x larger. And drag grows quadratically.

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You seem to be confusing force (thrust or drag) with energy (under which concept work and power comes). Don't. You'll be spared much grief.

Work done is force times distance.

$$ W = Fs $$

Power is work done divided by time

$$ P = W/t $$

When you double velocity, force quadruples. As does work.

$$ W_\text{new} = 4Fs = 4W $$

Time halves as well, with the following effect on power.

$$ P_\text{new} = 4W/0.5t = 8P $$

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  • $\begingroup$ Whoever just edited. Make a superficial edit again so your name can be seen. You're the victim of an unfortunate coincidence $\endgroup$ Commented Feb 11, 2021 at 8:31
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    $\begingroup$ No need to see my name (it is still in the edit history) ;) $\endgroup$
    – Bianfable
    Commented Feb 11, 2021 at 8:35
  • $\begingroup$ power vs force solves it. I was missing the distinction. yes drag force goes up with the square, but power goes up another 2x because times goes down 2x. $\endgroup$
    – kaz
    Commented Feb 11, 2021 at 9:00

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