Can She Make It Through the Intersection Before the Light Turns Red?

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SUMMARY

The discussion focuses on a driving scenario where a driver approaches a yellow traffic light at 47 km/h, 30 meters from the intersection, which is 15 meters wide. The yellow light lasts for 2.0 seconds, and the car can decelerate at -6.2 m/s² or accelerate from 47 km/h to 70 km/h in 6.9 seconds. Calculating the stopping distance reveals that if she brakes, she will stop before the intersection, while accelerating allows her to cross before the light turns red.

PREREQUISITES
  • Understanding of basic kinematics, including acceleration and deceleration.
  • Familiarity with the equations of motion for constant acceleration.
  • Knowledge of unit conversions, particularly between km/h and m/s.
  • Ability to analyze traffic light timing and its implications on vehicle movement.
NEXT STEPS
  • Calculate stopping distance using the formula: d = v² / (2 * a).
  • Learn about the physics of acceleration and deceleration in vehicles.
  • Explore real-world applications of kinematics in traffic scenarios.
  • Investigate the impact of reaction time on driving decisions at traffic signals.
USEFUL FOR

Students studying physics, driving instructors, traffic safety analysts, and anyone interested in the practical applications of kinematics in driving scenarios.

stephidjadi
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A person driving her car at 47 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 -6.2 m/s2, whereas it can accelerate from 47 km/h to 70 km/h in 6.9 s. Ignore the length of her car and her reaction time.

a.If she hits the brakes, how far will she travel before stopping?

b. If she hits the gas instead, how far will she travel before the light turns red?
 
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stephidjadi said:
A person driving her car at 47 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 -6.2 m/s2, whereas it can accelerate from 47 km/h to 70 km/h in 6.9 s. Ignore the length of her car and her reaction time.

a.If she hits the brakes, how far will she travel before stopping?

b. If she hits the gas instead, how far will she travel before the light turns red?

Welcome to PF.

How would you start to solve the problem?
 

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