An Object with Mass M Is Dropped from Rest and We

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 $v = s ^ { \prime } ( t )$ 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.

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