I'm working on this project that involves air drag. The model for the air drag is given as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \vec F_d = \frac{1}{2} C \rho A v^2 [/tex]

I'm using Newton's Second law in relation to this force and gravity (in one dimension) which yields:

[tex] a = \frac{1}{m} \left( -mg + \frac{1}{2} C \rho A v^2 \right) [/tex]

I'm in the middle of an ODE course, so I have not dealt with anything nonlinear... so this is where my question is. If I convert everything to the differential form:

[tex] a = \frac{d^2x}{dt^2} [/tex]

[tex] v = \frac{dx}{dt} [/tex]

So what does [tex] v [/tex] become in the [tex] \vec F_d [/tex] equation?

It is [tex] \left( \frac{dx}{dt} \right)^2 [/tex]. I've just never encountered this. Does it become?

[tex] \frac{dx^2}{dt} [/tex]

thanks in advance

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# DIFFEQ - (probably a stupid question)

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