$14.$ A $160$ mm diameter pipe of mass $6$ kg rests on a $1\mathrm{.}5$ kg plate. The pipe and plate are initially at rest when a force P of magnitude $25$ N is applied for $0\mathrm{.}75$ s $.$ Knowing that $\backslash (\backslash$mu$\_\{\backslash$mathrm$\{$s$\}\}=0\mathrm{.}25\backslash )\backslash$& $\backslash (\backslash$mu$\_\{\backslash$mathrm$\{$k$\}\}=0,20\backslash )$ between the plate and both the pipe and the floor, determine;

$($a$)$ whether the pipe slides with respect to the plate.

$($b$)$ the resulting velocities of the pipe and of the plate.