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Statement of a problem № 22

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The velocity of a particle moving in the positive direction of the x axis varies as v = α sqrt(x), where α is a positive constant. Assuming that at the moment t = 0 the particle was located at the point x = 0, find: (a) the time dependence of the velocity and the acceleration of the particle; (b) the mean velocity of the particle averaged over the time that the particle takes to cover the first s metres of the path.

Solution:
The velocity of a particle moving in the positive direction of the x axis varies

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