Aparticle slides frictionlessly along a path in a vertical plane from point a to a lower point b under the force of gravity. the brachistochrone problem is to find the path that gives the minimum travel time when the particle starts from rest at a. find a solution for the path. you can take point a to be the origin of your coordinate system hint: you should find that you need to evaluate an integral of form v2 dy, where a is a constant. make the substitution y = a(1-cos θ). this will allow you to find a parametric solution for the minimum time path in terms of θ