$3.$ An infinite flat plate located at $\backslash ($ y$=0\backslash )$ is stationary until $\backslash ($ t$=0\backslash )$ when it begins moving horizontally in the positive $\backslash ($ x $\backslash )-$direction at a constant speed $\backslash ($ U $\backslash ).$ This motion continues until $\backslash ($ t$=$T $\backslash )$ when the plate suddenly stops moving. Determine the fluid velocity field, $\backslash ($ u$($y$,$ t$)\backslash )$ for $\backslash ($ t$>$T $\backslash ).$ At what height above the plate does the peak velocity occur for $\backslash ($ t$>$T $\backslash )?[$Hint: the governing equation is linear so the superposition of solutions is possible.$]$