A person driving her car at 44 km/h approaches an intersection just as the traff

Question

A person driving her car at 44 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning to red, and she is 30 m away from the near side of the intersection (Fig. 2-29). The intersection is 15 m wide. Her car's maximum deceleration is -6.4 m/s2, whereas it can accelerate from 44 km/h to 70 km/h in 7.8 s. Ignore the length of her car and her reaction time.

If she hits the brakes, how far will she travel before stopping?
answer in meters

If she hits the gas instead, how far will she travel before the light turns red?
answer in meters

Explanation / Answer

v = 44 km/h = 44/3.6 m/s, t = 2.0 s

a1 = [(70 - 44)/3.6]/7.8 = 1.21 m/s2, a2 = -6.4 m/s2

If she hits the brakes, how far will she travel before stopping?
(0 - v2)(2a2) = 11.7 m

If she hits the gas instead, how far will she travel before the light turns red?
vt + a1t2/2 = 26.9 m

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