Hi. It's been 25 years since my last calculus class and I'm beyond rusty. I hope somebody her might be able to lend me a hand.
I'm working on a machine that discharges spherical solids horizontally in still air at a known speed. I'd like to study the sphere's speed over set time and/or distance intervals. The sphere will be slowed by aerodynamic drag. The standard drag formula D=.5 p (V^2) Cd A [where D is drag force, p is air density, V is velocity, Cd is coefficient of drag, and A is cross sectional area of sphere] can be used to determine the force that decelerates the sphere. As the force tending to decelerate the sphere is a function of velocity, it constantly decays after the sphere is discharged from the machine.
So I'm looking for an expression for V in terms of distance and an expression for V in terms of time.
I hope I've explained what I'm trying to do well enough. Let me know if I can clear up anything. Thanks.