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

question 2

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.

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Definitions:

Variable-ratio

A schedule of reinforcement where a response is reinforced after an unpredictable number of responses, making it highly resistant to extinction.

Reinforcement

An operational technique used in behavior analysis to increase the frequency of a desired behavior by introducing a motivating item after the behavior is exhibited.

DRH Schedule

Differential Reinforcement of High Rates of behavior schedule; a reinforcement schedule in which a higher rate of a specific behavior is reinforced, encouraging the behavior to occur more frequently.

Reinforcer

Any stimulus that increases the likelihood of a preceding behavior being repeated.