Modelling using differential equations

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• Sep 24th 2008, 08:37 PM
njr008
Modelling using differential equations
A particle of mass m is released from rest at time t = 0 at some height above the ground. It experiences a resistance mkv where v is its speed and k a constant. Find v and the vertical distance fallen after time t.

I admit I am a little lost on this question, so any help would be appreciated.
• Sep 25th 2008, 04:13 AM
Showcase_22
I think it goes a little like this:

$\displaystyle F=ma$

$\displaystyle F=m\frac{dv}{dt}$

$\displaystyle mg-mkv=m\frac{dv}{dt}$

$\displaystyle g-kv=\frac{dv}{dt}$

Then it's separation of variables or integrating factor to get an equation for v in terms of t.
• Sep 25th 2008, 04:19 AM
mr fantastic
Quote:

Originally Posted by Showcase_22
I think it goes a little like this:

$\displaystyle F=ma$

$\displaystyle F=m\frac{dv}{dt}$

$\displaystyle mg-mkv=m\frac{dv}{dt}$

$\displaystyle g-kv=\frac{dv}{dt}$

Then it's separation of variables or integrating factor to get an equation for v in terms of t.

And once v = v(t) is got, it's not hard to get x = x(t) from it.