A runner travels on a circular path with velocity equation v(t) = 0.06t² + 0.15t, starting from rest. It took him 3.25 seconds to finish the first 5-meter run. Find the radius-of-curvature of the circular track if he achieves a total acceleration of 12 m/s² at the time he covered a distance of 28 meters.

A runner travels on a circular path with velocity equation v(t) = 0.06t² + 0.15t, starting from rest. It took him 3.25 seconds to finish the first 5-meter run. Find the radius-of-curvature of the circular track if he achieves a total acceleration of 12 m/s² at the time he covered a distance of 28 meters.