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 Post subject: Acceleration -Velocity Models of LinearPosted: Fri, 5 Sep 2003 03:05:53 UTC
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Joined: Fri, 5 Sep 2003 02:59:44 UTC
Posts: 19
Consider a body that moves horizontally through a medium whose resistance is proportional to the square of the velocity V, so that dv/dt = -kV^2. Show that
V(t) = Vo/ (1 + Vokt)
and taht
X(t) = Xo + 1/k ln(1 + Vokt).

NOte that, in contrast with the results of Problem 2, X(t) --> + infinity as t --> +infinity

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 Post subject: Re: Acceleration -Velocity Models of LinearPosted: Fri, 5 Sep 2003 04:43:27 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 8306
Location: Lexington, MA
Hello, beaversjoe!

Quote:
Consider a body that moves horizontally through a medium
whose resistance is proportional to the square of the velocity V,
so that dv/dt = -kV^2.
Show that: V(t) = Vo/ (1 + Vokt)
and that: X(t) = Xo + 1/k ln(1 + Vokt)

We have:

Integrating:

When

Then:

To find integrate

When

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