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

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The discussion focuses on calculating the time interval during which a bicycle leads a car after a traffic light turns green, given their respective accelerations and maximum speeds. The bicycle accelerates to 29.0 mi/h at 12.50 mi/h-s, while the car accelerates to 51.0 mi/h at 8.00 mi/h-s. The calculated time interval for the bicycle to be ahead of the car is 13.08 seconds, determined by analyzing when both vehicles reach their maximum speeds. The maximum distance the bicycle leads the car occurs when the car matches the bicycle's speed, after which the bicycle no longer gains distance. This analysis highlights the importance of understanding constant acceleration and relative speeds in traffic scenarios.
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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?
 
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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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