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Statement of a problem № 42

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A particle moves along the plane trajectory y(x) with velocity v whose modulus is constant. Find the acceleration of the particle at the point x = 0 and the curvature radius of the trajectory at that point if the trajectory has the form (a) of a parabola y = ax2; (b) of an ellipse (x/a)2 + (y/b)2 = 1; a and b are constants here.

Solution:
A particle moves along the plane trajectory y(x) with velocity v whose modulus i

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