Beta version!

A particle moves in a straight line whose acceleration \(a\) depends on the velocity \(v\) according to the equation \(a=-\alpha\sqrt{v}\), where \(\alpha\) is a positive constant.

At the initial moment, the velocity of the particle is \({v}_{0}\).

If the average speed just before it stops is \(\large{\frac{{v}_{0}}{\beta}}\), where \(\beta\) is a positive integer, find \(\beta\).

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