A person driving her car at 48 km/h approaches an intersection just as the traff

Question

A person driving her car at 48 km/h approaches an intersection just as the traffic light turns yellow. 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 -7.0 m/s2, whereas it can accelerate from 48 km/h to 70 km/h in 6.6 s. Ignore the length of her car and her reaction time.

1) If she hits the brakes, how far will she travel before stopping? (m)

2) If she hits the gas instead, how far will she travel before the light turns red? (m)

3) Should she try to stop, or should she speed up to cross the intersection before the light turns red?

Explanation / Answer

converting to proper units: vi = 48 km/hr = 13.33 m/s vf = 70 km/hr = 19.44 m/s 1) vf = vi + at 0 = 13.33 - 7.0t 7.0t = 13.33 t = 1.90 seconds d = vi(t) + 0.5at^2 d = 13.33(1.90) + 0.5(-7)(1.90^2) d = 12.7 m 2) vf = vi + at 19.44 = 13.33 + a(6.6) a = 0.926 m/s2 d = vi(t) + 0.5at^2 d = 13.33(2) + 0.5(0.926 )(2^2) d = 28.5 m 3) she should try to stop; if she accelerates to her top speed (which would take 6.6 seconds), she would only get to 28.5 m which is about 1.5 m before the intersection. bol

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