For an assignment of mine I am creating a very basic model of an airplane, where I choose to consider a fixed amount of parameters that affect flight and to disregard others which I find too difficult to model due to lack of experience. I am modelling the acceleration to start, and I've gotten this far:
$Acceleration = Force * Mass$
$Force = TotalThrust - Drag$
I have the total thrust for my model of airplane, the C-130 Hercules, however for drag is where complications arise. I wish to plot acceleration vs. time in a graph of mine to derive an equation of it, however I don't know how I would express drag as a function of time if somehow possible.
Being that the equation for Drag is the following:
$Drag = (Drag Coefficient) * (Density of Air) * (Terminal Velocity)^2 * (Area of Wing)$,
I was wondering if I could express either the density of air or terminal velocity as a function of time if somehow possible, so that I could create an acceleration vs. time graph. Is there any way at all to manipulate variables such that the expression becomes as a function of time?
Keep in mind I am making the primitive assumption that everything else stays fixed. I.e., if my terminal velocity becomes a function of time, I'll keep my drag coefficient, and density of air as fixed values just for the sake of making it less complicated.