There are two parts to the distance. The first part is the small distance the car travels before driver brakes s1=vxt=20m/sx0.53s . The second distance we find by integrating from point 1 where brakes are applied to point 2 where car stops. To do this we first write dv=a dt from definition of acceleration. And then manipulate definition of velocity to get dt = ds/v and substitute that into first equation to replace dt there. After we move the v in denominator over to other side we get v dv = a ds we integrate this from v1 of 20 m/s to v2 of 0 m/s on left and s1 of 0 to s2. We then solve for s2 and add it to first distance. Note that since s2 is zero some terms are zero and leaves only s2 as unknown.