Problem $4$: A $600$ lb crate $($B$)$ rests on the ground for which the ceefficients of static and kinetic friction are $\backslash (\backslash$mu$\_\{5\}=0\mathrm{.}5\backslash )$ and $\backslash (\backslash$mu$\_\{$k$\}=0\mathrm{.}4\backslash ),$ respectively. The winch detivers a horizontal towing force $\backslash ($ T $\backslash )$ to its cable at $\backslash ($ A $\backslash )$ which varies as shown in the graph. Determine the velocity of crate, $\backslash ($ B $\backslash )$ at $\backslash ($ t$=15\backslash )$ seconds. Originally the tension in the cable is zero. For more information, please refer to Figure $4.$

Figure $4$: Problem $4$