The $\backslash (15-\backslash$mathrm$\{$Mg$\}\backslash )$ boxcar $\backslash ($ A $\backslash )$ is coasting at $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ on the horizontal track when it encounters a $12-$Mg tank car $\backslash ($ B $\backslash )$ coasting at $\backslash (0\mathrm{.}75\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ toward it as shown in Fig. $15-8$a$.$ If the cars collide and couple together, determine $($a$)$ the speed of both cars just after the coupling, and $($b$)$ the average force between them if the coupling takes place in $0\mathrm{.}8$ s $.$