Answer
$\beta = 0.943$
Work Step by Step
We can find $\gamma$:
$K = (\gamma-1)~mc^2 = 2.00~E_0$
$\gamma-1 = \frac{2.00~E_0}{mc^2}$
$\gamma = 1+\frac{2.00~E_0}{E_0}$
$\gamma = 3.00$
We can find $\beta$:
$\gamma = \frac{1}{\sqrt{1-\beta^2}}$
$1-\beta^2 = \frac{1}{\gamma^2}$
$\beta^2 = 1-\frac{1}{\gamma^2}$
$\beta = \sqrt{1-\frac{1}{\gamma^2}}$
$\beta = \sqrt{1-\frac{1}{(3)^2}}$
$\beta = 0.943$
