Faster than light

Let $x$ be the fraction of the speed of light you are traveling at. By the theory of relativity, time is dilated by a factor of $\frac{1}{\sqrt{1-x^2}}$ . Thus, your apparent speed will be $\frac{xc}{\sqrt{1-x^2}}$ . The inequality then becomes $\frac{xc}{\sqrt{1-x^2}}>c$ , or $\frac{x}{\sqrt{1-x^2}}>1$ . This rearranges to $x>\sqrt{1-x^2}\rightarrow2x^2>1\rightarrow x>\frac{\sqrt{2}}{2}$ . Your speed must therefore be $3\times10^8\times\frac{\sqrt{2}}{2}=\boxed{2.12\times10^8}$ $m/s$ .