How Long Does a Bicycle Lead a Car After a Traffic Light Turns Green?

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SUMMARY

The discussion focuses on the dynamics of a bicycle and a car accelerating from rest after a traffic light turns green. The car accelerates to a maximum speed of 51.0 mi/h with a constant acceleration of 8.00 mi/h-s, while the bicycle accelerates to 29.0 mi/h with a constant acceleration of 12.50 mi/h-s. The bicycle leads the car for a time interval of 13.08 seconds, after which the car reaches its maximum speed. The maximum lead distance of the bicycle occurs when both vehicles reach their cruising speeds, with the bicycle maintaining a lead until that point.

PREREQUISITES
  • Understanding of constant acceleration equations, specifically xf=xi+vxi*t+1/2*ax*t^2
  • Knowledge of speed and time graph analysis
  • Familiarity with units of speed (mi/h) and acceleration (mi/h-s)
  • Basic principles of kinematics in physics
NEXT STEPS
  • Study the application of constant acceleration equations in real-world scenarios
  • Learn how to create and interpret speed/time graphs for various motion types
  • Explore the effects of different acceleration rates on lead distances in competitive scenarios
  • Investigate the implications of varying maximum speeds in vehicle dynamics
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of motion and acceleration in vehicles, particularly in scenarios involving comparative speeds and lead distances.

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Homework Statement


As soon as a traffic light turns green, a car speeds up from rest to 51.0 mi/h with constant acceleration 8.00 mi/h-s. In the adjoining bike lane, a cyclist speeds up from rest to 29.0 mi/h with constant acceleration 12.50 mi/h-s. Each vehicle maintains constant velocity after reaching its cruising speed.
(a) For what time interval is the bicycle ahead of the car?
(b) By what maximum distance does the bicycle lead the car?

Homework Equations



Constant acceleration equations specifically xf=xi+vxi*t+1/2*ax*t^2

The Attempt at a Solution


13.08 seconds as the answer to part A. by finding at what time the velocities are maxed out which is 2.32 and 6.75, respectively the bike and car. After this I set the xf of each equal to each other and solve for t. Any help?
 
Last edited:
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A speed/time graph is always a useful tool.

The maximum distance will be when the car reaches the same speed as the bicycle's maximum speed, that is when the bicycle is no longer pulling away from the car.
 

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