An object with mass $50$ kg has an initial downward velocity of $-30\frac{(m)}{(s)}.$ Assume that the atmosphere exerts a resistive force with magnitude proportional to the speed. The resistance is $-80N$ when the velocity is $-4\frac{(m)}{(s)}.$ Use $g=10\frac{(m)}{s^2}$

a$.$ Write out a differential equation in terms of the velocity $v,$ and acceleration $a$

b$.$ Find the velocity $v(t)$ for the object