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## Main Question or Discussion Point

Hello and thanks to all who read this. Recently I've just been messing around with air drag equations, trying to extend applied maths problems to include air drag. And I've hit a road block, at least with regards to my knowledge anyway.

I've been using the F_drag = 1/2 P (mass density of fluid) v^2 C_d (drag coefficient) A (area). But my problem with this equation is it's dependence on velocity. If I were to use this equation on a projectile which is under acceleration (under gravity, and also the air drag would slow down the velocity) it would change the initial velocity, making the equation useless to me (I think).

I guessed that air drag on an accelerating body would require a differential equation, so I tried to go about making one.

F = c.v^2 (c is just the constant of pressure, area and drag coefficient etc in the drag equation)

So, I got...

dP/dt = c.v^2

m(dv/dt) = c.v^2

dv/v^2 = c/m dt

Then I went about integrating this trying to get some kind of an equation. But to no avail. I don't have a great physics knowledge as I'm only in school; so could someone be so kind as to help me get an equation which could calculate the air drag on a body that is undergoing acceleration.

I don't know if I'm making much sense in this post; but thanks anyway!

Just thinking about it there: would the best method be to calculate the air drag on the projectile at various time intervals? I.e. every second, then recalculate the air drag at the new lower speed, then, a second later recalculate again? If you get what I mean.

I've been using the F_drag = 1/2 P (mass density of fluid) v^2 C_d (drag coefficient) A (area). But my problem with this equation is it's dependence on velocity. If I were to use this equation on a projectile which is under acceleration (under gravity, and also the air drag would slow down the velocity) it would change the initial velocity, making the equation useless to me (I think).

I guessed that air drag on an accelerating body would require a differential equation, so I tried to go about making one.

F = c.v^2 (c is just the constant of pressure, area and drag coefficient etc in the drag equation)

So, I got...

dP/dt = c.v^2

m(dv/dt) = c.v^2

dv/v^2 = c/m dt

Then I went about integrating this trying to get some kind of an equation. But to no avail. I don't have a great physics knowledge as I'm only in school; so could someone be so kind as to help me get an equation which could calculate the air drag on a body that is undergoing acceleration.

I don't know if I'm making much sense in this post; but thanks anyway!

Just thinking about it there: would the best method be to calculate the air drag on the projectile at various time intervals? I.e. every second, then recalculate the air drag at the new lower speed, then, a second later recalculate again? If you get what I mean.

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