Answer
$\beta = 8.2\times 10^{-8}$
Work Step by Step
We can express the speed in units of $m/s$:
$v = (55~mi/h)(\frac{1602~m}{1~mi})(\frac{1~h}{3600~s}) = 24.475~m/s$
We can find the speed parameter $\beta$:
$\beta = \frac{v}{c} = \frac{24.75~m/s}{3.0\times 10^8~m/s} = 8.2\times 10^{-8}$
