(Solution) - A particle moves in the plane xy with velocity v -(2025 Original AI-Free Solution)

Paper Details

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.