Question

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 11.7 m/s2 and a maximum speed of 109 m/s. Car B has an acceleration of 11.1 m/s2 and a maximum speed of 92.0 m/s. Which car wins the race, and by how many seconds?

Answer 1

Quarter of mile equals L = 402 m.
The car A accelerates during time t_a1 = v1/a1 = 109/11.7 = 9.31 s and covers a distance s1 = a1*t_a1^2/2 = 507 m. Thus, the total time of motion is T1 = sqrt(2L/a1) = 8.28 s.
In the same way car B accelerates during time t_a2 = 92/11.1 = 8.29 s and covers a distance s2 = 381 m. t_a2 < T1, thus the car A wins.