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)?

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