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 $s$.