The motor winds in the cable with a constant acceleration, such that the $\backslash (20-\backslash$mathrm$\{$kg$\}\backslash )$ crate moves a distance $\backslash (\backslash$mathrm$\{$s$\}=6\backslash$mathrm$\{$~m$\}\backslash )$ in $3$ s $,$ starting from rest as shown in Figure $5.$ Determine the tension developed in the cable. The coefficient of kinetic friction between the crate and the plane is $\backslash (\backslash$mu$\_\{\backslash$mathrm$\{$k$\}\}=0\mathrm{.}3\backslash ).$

$(25$ marks$)$