Curves & Motion · Superchallenge problem

The Cornu spiral is $\mathbf r(s) = \left(\displaystyle\int_0^s \cos\frac{u^2}{2}\,du,\ \int_0^s \sin\frac{u^2}{2}\,du\right)$, $s \ge 0$. Find its radius of curvature at the first point with $s > 0$ where its tangent line is vertical.