# 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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