# Really quick differential question

Lewis
If I am rewriting v in terms of x and t, I write it as dx/dt, but how about v^2?

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urnt? Are you talking about Reduction of order?
Like:

http://tutorial.math.lamar.edu/AllBrowsers/3401/ReductionofOrder_files/eq0021M.gif [Broken]

http://tutorial.math.lamar.edu/AllBrowsers/3401/ReductionofOrder_files/eq0022M.gif [Broken]

http://tutorial.math.lamar.edu/AllBrowsers/3401/ReductionofOrder_files/eq0023M.gif [Broken]

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Lewis
I don't know, my prof likes to ask questions on things he doesn't teach :\

I mean, in an equation like: F=-mv, you can rewrite it like m [(d^2 x)/(dt^2)] = -m dx/dt

But how would you rewrite F=-m(v^2) ?

$$(v)^2 = v*v$$
$$(\frac{dx}{dt})^2 = \frac{dx}{dt} * \frac{dx}{dt}$$

Let's say $x=t^2+t^4$ then $v = \frac{dx}{dt}$. So we then have $F = mv^2 = m \times \frac{dx}{dt} \frac{dx}{dt} = 2t+4t^3 \times 2t+4t^3$

assuming F = mv

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Lewis
Okay, thanks a lot!