Problem 1.41

A point moves in the plane so that its tangential acceleration \(w_{\tau}=a,\) and its normal acceleration \(w_{n}=b t^{4},\) where \(a\) 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 \(s\).