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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Imagine sticking your hand in a tub full of water. If you move it through the water very slowly there’s almost no resistance at all. If the water was exactly skin temperature and you closed your eyes, you’d scarcely even know that your hand was moving through water instead of air. Now move your hand as fast as can through the water. The resistance is now much, much greater. Clearly, it takes far more energy per stroke to move your hand through the water fast. It’s the same for the car moving through the air. Even though it only goes the same distance, if it’s going faster it takes more energy. Since that energy comes from burning fuel, you have to burn more fuel to go faster.
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