1. A coin with radius r is rolling on a surface without slipping in the positive x-direction as shown below. As the coin rolls, point P contacts the surface at the origin. a. Derive expressions for the position, velocity, and acceleration of point P with respect to the fixed reference frame N in terms of the angle 0. b. Derive expressions for the velocity and acceleration of point P at 9 = 0, ñ/2,л, 3л/2, 2π, and 4π. c. Describe the characteristics of each expression in part b above. d. If r = 0.25 m, plot the vertical position of point P as a function of 9 from 0 = 0 to 8 = 4π. e. On your plot from part d above, draw vectors representing the x and y components of velocity, and a vector representing the total velocity, of point P at е = 0, π/2, л, зл/2, 2л, and 4π. N y D 8 x