A disk, with a radius of $0\mathrm{.}25$ m$,$ is to be rotated like a merry$-$ go$-$round through $800$ rad, starting from rest, gaining angular speed at the constant rate a$1$ through the first $400$ rad and then losing an$-$ gular speed at the constant rate $\%$a$1$ until it is again at rest. The mag$-$ nitude of the centripetal acceleration of any portion of the disk is not to exceed $400$ m$/$s$2.($a$)$ What is the least time required for the ro$-$ tation? $($b$)$ What is the corresponding value of a$1?$