Freight trains can produce only relatively small accelerations. $($a$)$ What is the final velocity of a freight train that accelerates at a rate of $0\mathrm{.}0500$m$/$s$20\mathrm{.}0500$m$/$s$2$ for $8\mathrm{.}00$ min, starting with an initial velocity of $4\mathrm{.}00$ m$/$s$?($b$)$ If the train can slow down at a rate of $0\mathrm{.}550$m$/$s$20\mathrm{.}550$m$/$s$2,$ how long will it take to come to a stop from this velocity? $($c$)$ How far will it travel in each case?