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A person driving her car at 45 km/h approaches an intersection just as the traffic light
Chapter 2, Problem 32P(choose chapter or problem)
A person driving her car at 45 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 red, and she is 28 m away from the near side of the intersection (Fig. 2–31). Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 m wide. Her car’s maximum deceleration is –5.8 m/s2, whereas it can accelerate from 45 km/h to 65 km/h in 6.0 s. Ignore the length of her car and her reaction time.
Questions & Answers
QUESTION:
A person driving her car at 45 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 red, and she is 28 m away from the near side of the intersection (Fig. 2–31). Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 m wide. Her car’s maximum deceleration is –5.8 m/s2, whereas it can accelerate from 45 km/h to 65 km/h in 6.0 s. Ignore the length of her car and her reaction time.
ANSWER:
Solution 32P
Step 1 of 2
We have to find whether the person driving her car should try to stop or speed up to cross the intersection before the light turns red.
Trying to stop:
The car with initial velocity of 45 km/hr and maximum deceleration of
m/s2 has to stop in a 28 m displacement when the brakes are applied.
The distance traveled during the break can be calculated using the kinematic equation,
Thus,
= 13.5
Hence, she can stop the car in time.