Answer
$2.10\times10^{8}m/s$.
Work Step by Step
The problem asks for a speed such that the value of $\gamma$ is $\frac{1}{\sqrt{1-u^{2}/c^{2}}}=1.40$. That is the factor by which the length is contracted. The Denebian Empire logo would appear to be circular.
$u/c=\sqrt{1-(1/1.40)^2}=0.700$
$u =0.700(3.00\times10^{8}m/s) =2.10\times10^{8}m/s $
