# Thread: Modelling using differential equations

1. ## 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.

2. 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.

3. 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.