Problem $12\mathrm{.}13$

The position of a car as a function of time t$,$ with t$>0$ and expressed in seconds, is

vec$($r$)($t$)=[(66$t$-120)($hat$())+(1\mathrm{.}2+31\mathrm{.}7$t$-8\mathrm{.}71$t$^(2))($hat$())]$ft

If the speed limit is $55$ mph $,$ determine the time at which the car will exceed this limit$.$