A race car starts from rest on a circular track of radius 267 m. The car's speed increases at the constant rate of 0.420 m/s2.

A race car starts from rest on a circular track of radius 267 m. The car's speed increases at the constant rate of 0.420 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, find the following.