A circular wheel with radius 1 ft and center C rolls to the right along the x-axis at a half-turn per second. At time t seconds, the position vector of the point P on the wheel’s circumference is

a. Sketch the curve traced by P during the interval 0 ≤ t ≤ 3.

b. Find v and a at t = 0, 1, 2, and 3 and add these vectors to your sketch.

c. At any given time, what is the forward speed of the topmost point of the wheel? Of C?

r = (t sin #t)i + (1 - cos t)j. -