A private tech company built one of the most advanced and powerful particle accelerators ever. The accelerator uses electricity to 'push' the charged particles (electrons) along a circular path, making them go faster and faster. The path they follow is given by the equation r = v$\cdot$cos(kt²) î + v$\cdot$sin(kt²) ĵ, where v = 4 m and k = 7 x 10⁴ rad/s² are constants and t is the time. Determine the circle's radius.