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Statement of a problem № 35

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A particle moves in the plane xy with velocity v = ai + bxj, where i and j are the unit vectors of the x and y axes, and a and b are constants. At the initial moment of time the particle was located at the point x = y = 0. Find: (a) the equation of the particle s trajectory y(x); (b) the curvature radius of trajectory as a function of x.

Solution:
A particle moves in the plane xy with velocity v = ai + bxj, where i and j are t

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