The $\backslash (3\mathrm{.}800-\backslash$mathrm$\{$lb$\}\backslash )$ carriage $\backslash ($ ; C $\backslash )$ is supported as shown by two uniform $\backslash (2-\backslash$mathrm$\{$lb$\}\backslash )$ disks, each having a radius of $3$ in $.$ Knowing that the carriage is initially at rest, determine the velocity of the carriage $0\mathrm{.}5$ s after the $0\mathrm{.}2-$lb force $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ has been applied. Assume that the disks roll without sliding. $($Round the final answer to four decimal places.$)$

The velocity of the carriage is: ft$/$s $.$