Answer
$v = 0.60~c$
Work Step by Step
We can find the Lorentz factor $\gamma$:
$E = \gamma~m~c^2$
$\gamma = \frac{E}{m~c^2}$
$\gamma = \frac{1.02\times 10^{-13}~J}{(9.1\times 10^{-31}~kg)~(3.0\times 10^8~m/s)^2}$
$\gamma = 1.245$
We can find the speed:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$\sqrt{1-\frac{v^2}{c^2}} = \frac{1}{\gamma}$
$1-\frac{v^2}{c^2} = (\frac{1}{\gamma})^2$
$\frac{v^2}{c^2} = 1-(\frac{1}{\gamma})^2$
$v = \sqrt{1-(\frac{1}{\gamma})^2}~c$
$v = \sqrt{1-(\frac{1}{1.245})^2}~c$
$v = 0.60~c$
