Use the <pion> <rest energy> supplied through its electron-mass ratio:
$$
m_\pi c^2=273(0.51\,\mathrm{MeV})=139.23\,\mathrm{MeV},\qquad
\gamma=1+\frac{K}{m_\pi c^2}=1.71824.
$$
Thus
$$
\boxed{v=c\sqrt{1-\gamma^{-2}}=0.813c\simeq2.44\times10^8\,\mathrm{m\,s^{-1}}.}
$$

Solution

Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / Section A / 6 / a / Solution

 Solution (source code)