# Find value of a variable from measured data

I have a measurement from which I want to deduct the value of a physical size (velocity). The theoretical equation is $$A\frac{(b+vt)^2}{(c-vt)^2}$$

Where $A$, $b$ and $c$ are all known sizes, $t$ is the time variable and $v$ is the wanted size. Which curve should I approximate the measured data in order to find $v$?

-

$y_t = A \dfrac{(b+vt)^2}{(c-vt)^2}$
$\sqrt {y_t/A} = \dfrac{b+vt}{c-vt}$
Let $u_t = \sqrt {y_t/A}$
$vt(1+u_t) = cu_t-b$