$1-$ A $1000$ kN column load is to be supported by a rectangular footing, $2$ m deep, underlain by young, uncemented, normally consolidated sandy soils. A representative CPT sounding for the site has been provided below. The groundwater table is located at a depth of $3$ m $,$ with the soil unit weight being $\backslash (18\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ above the groundwater table and $\backslash (20\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ below. Determine the most optimal dimensions for the foundation to resist bearing capacity failure with a factor of safety of $2\mathrm{.}5,$ considering that the foundation length is limited to a maximum of $5$ m due to land geometry constraints. Additionally, estimate the time required after construction for the total settlement of this footing to reach $15$ mm $.$ Make reasonable assumptions for any missing data.