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**Hard Kinematics Question- Please Help!**

## Homework Statement

When placing traffic lights at an intersections, planners have to determine how long the yellow light should stay on. This will depend on the speed limit on the road and on the length of the intersection. Outside a building,on the intersection there is a traffic light. For cars travelling alont the intersection, the speed limit is 50km/h. The distance to cross the intersection (pedestrian) is 34m. The length of a normal car is 4.5m. For safety reason, it is recommended vehicles stop with an acceleration no higher than 3.0m/s^2 (backwards [-3.0m/s^2]). Determine how long the yellow light should be at the intersection. You must include the following questions.

## Homework Equations

1. How much distance (in meters) will it take a car to stop when a light turns yellow if it is travelling at the speed of 50 km/h? Drivers do not react right taway when they see the light change. Assume that the driver does not react for 1.0s. In other words, the car continues to travel at the speed limit for 1.0s after the light has turned. Then the driver brakes to a stop at an acceleration of 3.0m/s2 (backward). What total distance will the car need to stop including reactiong time?

2. Using your results from the previous question, determine how long the yellow light needs to be to allow vehicles that are close to stop to continue at the speed limit and clear the intersection before the light turns read.

Modern car tires allow cars to stop at an acceleration of 10m/s^2 (backwards) without loosing control. This would allow you to shorten the yellow light time. Is this a good idea? What other factors will determine the stopping distance of a car?

## The Attempt at a Solution

Just trying to check my answer. I would appreciate if you yould write the answer along with the your methods. Please use kinematics equations! Thank you :)

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