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A common equation you will find in aerodynamics texts is:

Drag = 1/2 * fluid density * velocity^2 * C_d * Ref. Area

It approximates the drag experienced by objects as they move within a fluid (atmosphere). You can see that drag is proportional to the square of velocity, so going twice as fast induces 4 times the drag.

Ergo, when you speed up, you produce a lot more drag. This will slow you down until you reach an equilibrium between thrust and drag (unless you apply more thrust).



So you're just agreeing with what I said:

> I think what he's getting at is that drag increases with the square of speed




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