I think I understand that driving faster increases drag because there’s more air pushing against your vehicle, but why is the drag for that distance greater at higher speeds? If a car is driving slower but across the same distance, wouldn’t the total impulse created by the drag be the same as going faster because it’s delivered over a greater time, even though it’s a smaller force at any given moment?
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Impulse causes change in momentum, but this is about energy. The important quantity is work = force times distance. The distance of your trip is the same no matter how fast you go, but higher speed means more drag force means more work done and more energy lost to drag.
This would be true regardless of how force increased with speed: the fact that it increases with the square of speed, as mentioned by others, makes it worse.
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