Going down the parabolic slide

Under the influence of gravity ($$g = \SI[per-mode=symbol]{10}{\meter\per\second\squared}$$), a bead slides down a friction-less wire in the shape of the curve $$y = x^{2}$$. The bead begins from rest at $$(x,y) = (\sqrt{2}\si{\meter},\SI{2}{\meter})$$.

How much time (in seconds) does it take the bead to travel from the point $$(\SI{1}{\meter},\SI{1}{\meter})$$ to the origin $$\left(\SI{0}{\meter},\SI{0}{\meter}\right)$$ (to 2 decimal places)?

×