How to solve $$\frac{dv}{dt} = av^2 + bv + c$$ to obtain $x(t)$, where $a$, $b$ and $c$ are constants, $v$ is velocity, $t$ is time and $x$ is position. Boundaries for the first integral are $v_0$, $v_t$ and $0$, $t$ and boundaries for the second integral are $0$, $x_{max}$ and $0$, $t$.
What is the $x(t)$ function of $\dot{v} = a v² + bv + c$ to obtain $x(t)$
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integration
physics
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1I am guessing the second term should be $b v$? – 2012-05-15
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0Why don't you ask on [physics](http://physics.stackexchange.com/)? You'll get better answers, I think. – 2012-05-15
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0Yes you'r right the second term is bv. I posted it on physics too but they proposed me to post it on maths. – 2012-05-15
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0Am I right in assuming that the *speed* varies in your example, i.e., we need to solve a differential equation for speed and then integrate? – 2012-05-15
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3Solve for $v(t)$ by separation of variables; then integrate to get $x(t)$. – 2012-05-15