Express the x and y coordinate as a function of time

Question

1)     Consider a point P on the circumference of a wheel with radius 3m. At t = 0, the wheel is standing still leaning against y axis and x axis. This means center is at (3, 3) coordinates. Suppose at t = 0 the radius from center to P makes a 0 angle with the positive x axis, and the wheel starts rolling with constant angular velocity, making 1 revolution every 2 seconds, on the positive x direction on a road.

a)     Express the x coordinate of P as a function of time.

b)     Express the y coordinate of P as a function of time.

c)      Determine the coordinates of P at t = 5s

Answer 1

x = 3(t - sin t)

y = 3(1 - cos t)