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Question

Resistance of air acting on a falling body can be taken into account by the approximate relation for the acceleration:

$a=\frac{d v}{d t}=g-k v,$

where $k$ is a constant. Derive a formula for the velocity of the body as a function of time assuming it starts from rest $(v=0$ at $t=0)$. [Hint: Change variables by setting $u=g-k v$.]

Solution

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Answered 2 years ago

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1 of 10In this problem, motion in presence of air resistance is considered. The acceleration of a falling body is not only $g$, but it has a second term that is proportional to the speed of the body. The reader is asked to derive a formula for the velocity of the body as a function of time assuming it starts from rest ($v=0$ at $t = 0$).

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