The $3\mathrm{.}200-$lb carriage $\backslash ($ ; C $\backslash )$ is supported as shown by two uniform $2-$lb 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

$\backslash (\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ).$