Question #47244

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?

Expert's answer

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.

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.

## Comments

Assignment Expert18.09.15, 16:48Dear visitor,

please use panel for submitting new questions

Assignment Expert18.09.15, 16:47Thank you, we corrected the answer.

Dan11.09.15, 22:54There was a track distance given, it says a quarter of a mile. That makes this answer not correct.

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