An Object with Mass M Is Dropped from Rest and We

question 37

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

Vertebrate Lineages

Evolutionary branches that include all species descending from a common ancestor having a backbone or spinal column.

Tectonic Plate

Massive, irregularly shaped slab of solid rock, generally composed of both continental and oceanic lithosphere, which moves atop the earth's mantle.

Hot Spots

Areas of the Earth's mantle that are exceptionally hot, which can lead to volcanic activity on the surface.

Shelled Arthropod

Arthropods that have an external skeleton or shell, such as crustaceans and certain insects, providing protection and support.