Two cars start from rest at a red stop light. when the light turns green, both cars accelerate forward. the blue car accelerates uniformly at a rate of 3.8 m/s2 for 4.6 seconds. it then continues at a constant speed for 9.2 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 257.71 meters from where it started. the yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop.
how far does the blue car travel before its breaks are applied to slow down?