Yep. You're right. I should have remembered that.
Like your "car stopping distance" experiment, I've seen one involving ball bearings falling into fine sand. If the ball bearing's speed doubles, it goes four times as deep.
Correct me if I'm wrong, but doubling the speed of wind should therefore MORE than quadruple its force. More molecules per second and vastly more energy per molecule.
Squaring of speed to determine energy ties directly to Einstein's E=mc² formula, btw - in which, again, the energy derived is a function of the square of the speed.
Thanks for catching my gaff.