Deriving Expression for Average Drag on Object - Help Needed

[lithium123]

I'm trying to derive an expression for the average drag on an object, which is in the form $$F_d = kv^2.$$ To find the average, I decided to use $$\frac{1}{t_f} \cdot \int_{0}^{t_f} k v^2 \hspace{1mm} dt$$where t_f is the final time. I'm having trouble evaluating this. Can someone give me some insight?

 

[Simon Bridge]

To find the time average, you need the integrand to be a function of time.
So you need an expression for v(t) .

 

[paralleltransport]

Additional hint, there's a cool equation called
$$F = m {dv \over dt} ... = -kv^2$$

Can you solve for v(t) given than equation?