An object is coasting on the horizontal axis, in the positive direction and is subject to a drag force f = -bv - cv[tex]^{2}[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Write down Newton's 2nd Law and solve for v using separation of variables.

So first I wrote out Newton's law as:

F= m(dv/dt) = -bv - cv[tex]^{2}[/tex]

Solving the integral: dt = [tex]\frac{dv}{-bv-cv^{2}}[/tex], with boundaries from 0 to t and v(0) to v

I got: t = [tex]\frac{-m}{b}[/tex] ln[tex]\frac{v}{1+\frac{c}{b}v^{2}}[/tex]

Note: I haven't put in my boundaries on v yet. However, Once I put in my boundaries on v and try to rearrange to solve for v, I can't get anywhere. Any suggestions or help would be greatly appreciated.

Thx, CB

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# Homework Help: Both Quadratic and Linear Drag

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