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?


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 $t$.

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.