An Object with Mass $m$ Is Dropped from Rest and We Assume That the Air

Short Answer

An object with mass $m$ is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If $s ( t )$ is the distance dropped after $t$ seconds, then the speed is $v = s ^ { t } ( t )$ and the acceleration is $a = v ^ { \prime } ( t )$ . If $g$ is the acceleration due to gravity, then the downward force on the object is $m g - c v$ , where $c$ is a positive constant, and Newton's Second Law gives $m \frac { d v } { d t } = m g - c v$ .
Find the limiting velocity.