A steel sphere falls inside of a beaker containing a fluid whose force exerted on the sphere is given by $kv$. Assuming that the sphere starts from rest, calculate the falling speed.

The alternatives given by my book are as follows:

$\begin{array}{ll}

1.&\frac{mg}{4K}\left(1-e^{-\frac{k}{m}t}\right)\\

2.&\frac{mg}{2K}\left(1-e^{-\frac{k}{m}t}\right)\\

3.&\frac{mg}{K}e^{-\frac{k}{m}t}\\

4.&\frac{mg}{2K}e^{-\frac{k}{m}t}\\

5.&\frac{mg}{K}\left(1-e^{-\frac{k}{m}t}\right)\\

\end{array}$

How exactly should I assess this problem? Since all alternatives appear an exponential, I believe the approach does involve the use of drag.

The forces acting in the object would be as follows?

$F_{net}=mg-kv$

But I'm stuck there. I'm assuming that there's an integral which will cause the exponential to appear. But I don't know how to get there. Can someone help me?

I don't know exactly how to relate it with the fact that the object begins from rest. How would it be? Help please!