Problem: In a quarter-mile drag race, two cars start simultaneously from rest, and each accelerates at a constant rate until it either reaches its maximum speed or crosses the finish line. Car A has an acceleration of 11.4 m/s2 and a maximum speed of 103 m/s. Car B has an acceleration of 11.7 m/s2 and a maximum speed of 90.0 m/s.
Part A: Which car wins the race, and by how many seconds?
Please provide clear step by step solution with notes on concepts and equations being used.