The Air Resistance of a Free Falling Object Is Proportional $v ( t ) = 32 \left( e ^ { - p t } - 1 \right)$

question 60

Essay

The air resistance of a free falling object is proportional to its velocity. Use the equation of downward velocity given by $v ( t ) = 32 \left( e ^ { - p t } - 1 \right)$ , where $t$ is time and $v$ is measured in ft/s, to find the following.
(a) The initial velocity of the object.
(b) The velocity of the object after $2$ s and
$10$ s, if
$p = 0.25$ .
(c) The object's maximum or terminal velocity, and a graph of the object's velocity.

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