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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Drag increases with the square of your speed. If you double your speed, the drag *quadruples*. So yeah, you also get their twice as fast, but the total impulse from the drag force is still double what it would have been, had you driven at half the speed and taken twice as long.
For instance, let’s say at 30 mph you experience a drag of 10 (these are made-up numbers so I’m not going to dignify them with units), and you’re taking a 30-mile trip. The trip takes you 1 hour = 3600 seconds, yielding a total impulse of 36,000. Now let’s say you double your speed to 60 mph. This quadruples your drag to 40, while cutting your travel time in half to 1800 seconds, for a total impulse of 40*1800=72,000.
This is part of the story. Another part is due to the efficiency of your engine, which isn’t the same for all RPMs. There’s some optimal range. If you’re in a low gear and getting above the optimal RPM range, you can shift up a gear. But once you’re in your car’s top gear, you can’t do that any more. So, once you’re in the top gear and in the optimal RPM range, going any faster will inevitably make your car operate less efficiently.
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