Determining Yellow Light Timing for Intersection Safety

[ilovephysics9]

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 traveling 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 traveling 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 :)

 

[Doc Al]

Just trying to check my answer, and the way of working. I would appreciate if you yould write the answer along with the your methods. Please use kinematics equations!

You first! (Show your work and you'll get plenty of help.)

 

[ilovephysics9]

Errr... i got 25m for the first one. by the looks of it, it seems wrong. Anyone else wana help? :(

 

[Doc Al]

Show your work. Don't just give an answer, show how you got it.

 

[ilovephysics9]

I actually got 30m for the first question. I don't understand the 2nd question. For the first one, I found time by v2-v1/ a= t. I added 1s to the answer due to reaction time. V2 is 0.. v1 is 13.9m/s (50 km/h). I then substituted my findings into the equation d= v1 t + 1/2 a t ^2. Which led me to this answer.. Does this help dr. al? Anyone else? :)

 

[Doc Al]

For the first one, I found time by v2-v1/ a= t. I added 1s to the answer due to reaction time. V2 is 0.. v1 is 13.9m/s (50 km/h). I then substituted my findings into the equation d= v1 t + 1/2 a t ^2. Which led me to this answer..

Instead of adding the times, you need to add the distances. Find the distance traveled in the first second (before the brakes are applied), then find the distance it takes to stop once the brakes are applied. Add those two distances to get the total distance.

 

[ilovephysics9]

Thanks Doc Al.. i checked with my physics teacher and that is what he said! :). And for #2.. i added all distances (crosswalk + car + distance traveled by car) and divided them by v1 (speeds at which cars usually travel). Would that measure how long a yellow light will be on? And I can't get anything for #3.. any suggestions. Thanks :)