I don't understand how terminal velocity works. Help?

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Okay I understand that as velocity increases, so does the drag force. However, the drag force has to have a faster rate of increase compared to the velocity's rate of increase, otherwise the forces would never balance. But then I don't understand how when terminal velocity is reached, the drag force doesn't start to become bigger than the velocity. 

Think of this as two lines.
gradient = rate of increase in speed
Meeting point = terminal velocity.

If they were parallel, they would never meet. So they have to have different gradients (different rates of increase in speed). However after they meet, they part ways again. They don't keep together. Surely this would be like terminal velocity, wouldn't it? After an object reaches terminal velocity, it wouldn't stay like that. Someone please explain.

Posted Sun 10th June, 2012 @ 17:25 by Aparna

2 Answers

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Very thorough analysis here! haha, I wish I was this good at Phys! 
At the meeting point of your two gradients; it is where TV is reached, yes?

But the gradients are different because of the accelerating force (gravity) and your weight - this is pretty much constant. While we accelerate we create more drag as a reaction force and therefore an increasingly steeper gradient. Once the two forces have been equalled, we don't accelerate any more, so we have a constant velocity - thus giving a constant straight line on your theoretical axis. Because we are no longer accelerating there is therefore a constant amount of drag reacting against the falling object - again, producing the straight line on your axis. Because it occurs at the point of TV (your meeting point) the gradient functions of both your lines; (drag and acceleration) would be one constant line on your Y axis. 

I hope this helps! Message me if you need me to rephrase it or something. It all depends if I'm visualising it right!

Answered Sun 10th June, 2012 @ 19:52 by Sophie :o)
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oh wow, you're the one good at physics here! thanks i think i get it now. because the two forces are dependent on each other, when resultant force equals zero, the drag force remains the same to (kind of) match with the weight.

Answered Mon 11th June, 2012 @ 22:55 by Aparna