Mary is driving her car at 42 km/h. She approaches an intersection just as the t
ID: 2048320 • Letter: M
Question
Mary is driving her car at 42 km/h. She approaches an intersection just as the traffic light turns yellow. The yellow light lasts only 3.0 s before turning to red, and she is 30 m away from the near side of the intersection. The intersection is 15 m wide. Her car's maximum deceleration is -6.0 m/s^2, whereas it can accelerate from 42 km/h to 70 km/h in 8.4 s. Ignore the length of her car and her reaction time.
If she hits the brakes, how far will she travel before stopping? (m)
If she hits the gas instead, how far will she travel before the light turns red? (m)
Should she try to stop, or should she speed up to cross the intersection before the light turns red?
Explanation / Answer
42 km/h = 11.7 m/s
a) Time to stop = 11.7/6 = 1.95s
x = vt + 0.5at^2 = 11.7*1.95 - 3*1.95^2 = 11.4m
b)
v = 28 km/h =7.8 m/s
a = v/t = 2.6
d = vt + 0.5at2 = 11.7*3 + 1.3*9 = 46.8 m
c) She should speed up