If a free-falling body is not subject to air resistance, there is a linear relationship between v and t giving a line with constant slope (g) showing velocity increasing with time. If air resistance is taken into account, my guess is that acceleration will decrease until the terminal velocity is reached (i.e. where air resistance = weight of body) giving a curve with decreasing slope which flattens out to constant velocity. Is this correct or am I barking up the wrong tree? I made certain assumptions i.e that the body is heavy with a large surface area. I know that the curve for a feather would look different!
Yes, that's correct. You can't be a whole lot more precise. For small objects, the air-resistance is reasonably close to being proportional to the speed: instead of f= -mg you have f= -mg- kv. For larger objects, such as your feather, it's closer to being proportional to v^{2}: f= -mg+ kv^{2}. (The difference in sign is to keep the air resistance upward. If a body is falling downward, v is negative but v^{2} is positive.)