To expand on the “why does air resistance increase with the square of speed, and not just with speed?”
Intuitively, you can think of it like this: when you double the speed, you have to double the force your car is pushing the air out of the way. But on top of that, you are also pushing ***twice*** the air out of the way (because you are going twice as fast).
So one factor of speed comes from the speed you have to push the air and the second factor of speed comes from the amount of air you have to push. Two factor of speed is just speed squared, exactly as claimed.
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