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How to find velocity and displacement equations from a given force equation? For instance, it was given the following 1-D equation:

$$F = b_1(v_1-v) - b_2 v$$

$v_1$, $b_1$ and $b_2$ are constants.

I know that $F = ma = m\frac{\mathrm{d}v}{\mathrm{d}t}$, but I can't find how to integrate $F$. Is there any technique that can help me or my problem is just calculus?

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up vote 3 down vote accepted

Start with $$ m{dv\over dt}=b_1(v_1-v)-b_2v. $$ Move everything involving $v$ to one side of the equation, and everything involving $t$ (in this case, just $dt$) to the other side. Integrate both sides. One side will be just $\int dt$, or $t+C$. The other side will be some function of $v$. Algebraically solve the result to get $v$ in terms of $t$.

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Thanks! So, I have to use differential equations to solve these problems. –  Fábio Perez Mar 18 '11 at 0:08
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