Solve Problem at Traffic Intersection: Can You Make It Through?

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SUMMARY

The problem involves calculating whether a car traveling at the speed limit of 50 km/h can pass through three traffic lights without stopping, given that all lights turn green when the car is 10m away from the first intersection. The lights remain green for 13 seconds. The distances between the lights are 55m and 85m, respectively. The calculations show that the first car can pass through all lights without stopping, while the second car, which accelerates at 2.0 m/s² from a stop, can also make it through all three lights without stopping if it accelerates effectively.

PREREQUISITES
  • Understanding of basic kinematics, including distance, speed, and acceleration.
  • Knowledge of the formula for calculating time based on distance and speed.
  • Familiarity with the concept of traffic signal timing and its impact on vehicle movement.
  • Ability to perform calculations involving acceleration and final velocity.
NEXT STEPS
  • Study kinematic equations for uniformly accelerated motion.
  • Learn about traffic signal timing strategies and their effects on traffic flow.
  • Explore simulations of traffic intersections to visualize vehicle movement and signal changes.
  • Investigate the impact of different acceleration rates on traffic light compliance.
USEFUL FOR

Traffic engineers, physics students, automotive engineers, and anyone interested in traffic management and vehicle dynamics.

sens_freak_18
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Each intersection has a traffic signal and the speed limit it 50km/h. Suppose you are driving from west at speed limit. When you are 10m from the first intersection all lights turn green. The lights are green for 13 seconds each. (a) calculate time needed to reach third stop light. Can you make it through all three lights without stopping? (b) Another car was stopped at first light when all the lights turned green. It can accelerate at the rate of 2.0m/s^2 to the speed limit. Can the second car make it through all three lights without stopping? From first light to the second light the distance is 55m. from the second light to third light distance is 85m.

Any help is greatly appreciated!
 
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