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In physics book which I use right now proposes a simple deduction for drag equation. Almost every part of it is nice. But when deducting, it says: Whenever object hits an air molecule (which we assume to be stationary before the collision) it accelerates it to velocity $v$. In here, $v$ is velocity of a falling object through air.

The thing made me confused is part that says implicitly, "air molecules accelerate into velocity $v$" It's like author assumes it. (Like an assumption) But shouldn't, since molecules' mass is so less than free falling object, molecules must accelerate into much higher velocities compared to $v$?

I mean, electrons are very sensitive, and also, molecules are sensitive like electrons -but not exactly as electrons are-. Electrons go frenzy when they are interacted ,and with that, shouldn't molecules go frenzy; not as the same degree as electrons but you know, much higher velocities than just $v$? Is this a reasonable assumption -that molecules of air accelerate to $v$- when deriving drag equation, or I am missing a point? Can you help me? Thanks from now.

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yes molecules are a little frenzy / vibrate, but their average velocity is 0 (for example the air in a room doesn't move from a macroscopic view). Likely the author is assuming that the falling object is dragging with him(they don't bounce) the air molecules , that start with an average velocity v = 0 and then accelerate at the same speed of the falling object.

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