When an object moves through a medium (either a liquid or a gas), the medium exerts a resistive force $R$ on it.

We can model the resistive force in two ways.

### $R$ is proportional to $v$

$R=−bv$

### $R$ is proportional to $v_{2}$

$R=21 DρAv_{2}$
$D$ is a dimensionless empirical quantity called the *drag coefficient*
$ρ$ is the density of the medium (air most of the time)
$A$ is the cross-sectional area of the object
$v$ is the speed of the object

Finding terminal velocity $mg−R=ma$ $a=mmg−R $ At terminal velocity, the acceleration is 0. $mg−R=0$

$v_{T}=DρA2mg $