$(9\%)$ Problem $3$: A car accelerates in the $+$x direction from rest with a constant acceleration of a$\_\{1\}=1\mathrm{.}55$; m $/($s $^2)$ for t$\_\{1\}=20$ s$.$ At that point the driver notices a tree limb that has fallen on the road and brakes hard with a constant acceleration of a$\_\{2\}=-6\mathrm{.}74$m $/($s $^2)$ If the limb is on the road at a distance of $550$ meters from where the car begins its initial acceleration, will the car hit the limb$?$