MAT275 Modeling with First Order

We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude $c|v\left(t\right)|$ where $c=0.35\frac{kg}{s}$ and $v\left(t\right)$ is the velocity of the ball at time $t$. The gravitational constant is $g=9.8m/s^2$.

a) Find a differential equation for the velocity $v$:
$\frac{dv}{dt}=$−9.8−0.356|v|

b) Solve the differential equation in part a) and find a formula for the velocity at any time $t$:
$v\left(t\right)=$ 168.9−194.1e−0.058t

Find a formula for the position function at any time $t$, if the initial position is $s\left(0\right)=0$:
$s\left(t\right)=$ 3346.5e−0.058t−168.9t+3346.5

How does this compare with the solution to the equation for velocity when there is no air resistance?