1. The problem statement, all variables and given/known data A particle moves in a plane according to x= Rsin(wt) = wRt y= Rcos(wt) + R where w and R are constants. This curve, called a cycloid, is the path traced out by a point on the rim of a wheel which rolls without slipping along the x-axis. Question: (a) Sketch the path. (b) Calculate the instantaneous velocity and acceleration when the particle is at its maximum and minimum value of y. 2. Relevant equations x= Rsin(wt) = wRt y= Rcos(wt) + R 3. The attempt at a solution I drew up the path of the particle, as a cycloid of course. No problem with that. I am having problems understand part b, with relation to the curve. I differentiated the given equations wrt to x. i.e. dy/dt = -Rw sin (wt) dx/dt= Rw cos (wt) + wR then i proceed to find dy/dx = [Rw sin (wt)]/[Rw cos (wt) + wR] Ymaximum should be 2R (diameter of the rim of the wheel) I also went ahead to find values of x which corresponds to the maximum and minimum values of y. Values of X for maximum Y = 0, 2pie, ... Values of X for minimum Y = pie, 3pie, ... Instantaneous velocity is tangent of the curve of a position time graph, which is it the same as the graph i drew out? Then back to the original question, the instantaneous velocity at maximum y is therefore 0? and instantaneous velocity at minimum y is infinity? I know I have a conceptual error somewhere but I just can't figure it out.