Question

A person driving her car at 45 $\mathrm{km} / \mathrm{h}$ 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 28 $\mathrm{m}$ away from the near side of the intersection (Fig. 51). Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 $\mathrm{m}$ wide. Her car's maximum deceleration is $-5.8 \mathrm{m} / \mathrm{s}^{2}$ whereas it can accelerate from 45 $\mathrm{km} / \mathrm{h}$ to 65 $\mathrm{km} / \mathrm{h}$ in 6.0 $\mathrm{s}$ . Ignore the length of her car and her reaction time.

          A person driving her car at 45 $\mathrm{km} / \mathrm{h}$ 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 28 $\mathrm{m}$ away from the near side of the intersection (Fig. 51). Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 $\mathrm{m}$ wide. Her car's maximum deceleration is $-5.8 \mathrm{m} / \mathrm{s}^{2}$
whereas it can accelerate from 45 $\mathrm{km} / \mathrm{h}$ to 65 $\mathrm{km} / \mathrm{h}$ in 6.0 $\mathrm{s}$ . Ignore the length of her car and her reaction time.

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Added by Patrick W.

Physics: Principles with Applications

Douglas C. Giancoli 7th Edition

Chapter 2

Instant Answer

Solved by Expert Averell Hause

07/03/2019

Step 1

First, let's calculate the time it would take for the car to stop if she applied maximum deceleration. We can use the equation $v^2 = u^2 + 2as$, where $v$ is the final velocity (0 m/s), $u$ is the initial velocity (45 km/h), $a$ is the acceleration (-5.8 m/s^2), Show more…

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A person driving her car at 45 $\mathrm{km} / \mathrm{h}$ 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 28 $\mathrm{m}$ away from the near side of the intersection (Fig. 51). Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 $\mathrm{m}$ wide. Her car's maximum deceleration is $-5.8 \mathrm{m} / \mathrm{s}^{2}$ whereas it can accelerate from 45 $\mathrm{km} / \mathrm{h}$ to 65 $\mathrm{km} / \mathrm{h}$ in 6.0 $\mathrm{s}$ . Ignore the length of her car and her reaction time.

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