A point moves in the plane so that its tangential acceleration w = , and its normal

Question:

A point moves in the plane so that its tangential acceleration wτ = α, and its normal acceleration wn = bt4, where α and b are positive constants, and t is time. At the moment t = 0 the point was at rest. Find how the curvature radius R of the point's trajectory and the total acceleration w depend on the distance covered s.