A disk, with a radius of 0.25 m, is to be rotated like a merry-go-round through 1000 rad, starting from rest, gaining angular speed at the constant rate through the first 500 rad and then losing angular speed at the constant rate until it is again at rest. The magnitude of the centripetal acceleration of any portion of the disk is not to exceed 400 m/s².
(a) What is the least time required for the rotation?
(b) What is the corresponding value of α₁?