A person driving her car at 52 km/h approaches an intersection just as the traff

Question

A person driving her car at 52 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 -5.4 m/s2, whereas it can accelerate from 52 km/h to 70 km/h in 5.4 s. Ignore the length of her car and her reaction time.

Figure 2-29
http://www.webassign.net/giancoli5/2_29.gif

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

a.) If she hits the brakes she will travel: 52 km/h -> 14.4444444 m/s Vf^2 = Vi^2 + 2 * a * d 0 = 14.4444444^2 + 2 * (-5.4) * d d = 19.32 meters b.) If she hits the gas instead, she will travel: 70 km/h -> 19.4444444 m/s a = (19.4444444 - 14.4444444) / 5.4 = 0.926 m/s^2 d = Vi * t + (1/2) * a * t^2 d = 14.4444444 * 2 + (1/2) * 0.926 * 2^2 d = 30.74 m c.) She should stop since she has time to stop, but doesn't have time to make it through the intersection.

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