A wheel rotates in the clockwise (positive) direction and has no friction. The wheel is allowed to rotate for 4 seconds, then, at t=4s, a brake is applied so that the wheel slows down at a rate of alpha. At t=4s, alpha is zero but increases in magnitude linearly by 2 rad/s/s every second. The wheel stops in 4 s (at t=8s). Caloulate the initial angular speed of the wheel, and draw (with axis labels and scales) the omega vs. time and alpha vs. time (with correct signs) of the wheel for the 8 seconds described.