Running the red light (car physics)

[SamuraiTom]

Here a description of what I do to.

Your client was ticketed for running a red light but claims that he did not run the light. You must make a case to the judge explaining why your client was unjustifiably given a traffic citation for running a red light. You must determine the speed of the car, time interval for traffic light, a reference point with respect to the car, final position of the car, and maximum deceleration and acceleration of the car.

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The time interval between traffic lights
I have collected that data.

Trials Green Yellow Red
1 3.4 2.3 4
2 3.5 2.1 4
3 3.5 2.3 4
4 3.5 2.2 4
5 3.6 2.5 4

Average reaction time = .75 - 1.5 sec
Average deceleration rate = 3.4 m/s2

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I don't understand how to find the speed of the car which I think should have been given. It's a hypotheical situation where this happen. There is basically no data given about the car such as the speed, and mass of the car. I really need a push in the right direction. Can anyone give me tips onto approaching this very weird project?

 

[DaveC426913]

Tell us about that data you collected.
Do I read correctly? The light was green for only 3.4-3.6 seconds?

 

[SamuraiTom]

Yes, it's at an intersection by my school. Those lights goes by really fast, unless my stopwatch isn't working. The road coming out my school is fast, only a few cars can get past until it turns yellow to red.

Edit: I'm going to collect a new set of data to see if it similar to my first set tomorrow. Average speed is distance/time but the question doesn't give any numbers to work with. It doesn't say where he was stop past the intersection. It just say to determine everything without giving some bit of information.

 

[Farsight]

Tom: Find or assume the distance of the junction. Imagine a scenario, such as the client stopped at the lights. It turns red, he takes a second or so to react, and then he starts accelerating at 10 feet per second per second. He doesn't have time to get across the junction before it comes up red. Another possible scenario might be the client approaching the junction at say 30mph (44 fps) when the lights change but he doesn't have time to stop and crosses the junction mainly on red.

 

[caseys]

Never mind the mass of the car...you will not need if for the calculations you are trying to figure out.

Here are some formulas to use...

Speed = square root of (30df)

30 is a constant resulting in the derivation of this formula.
d is the distance if the vehicle is sliding (skidding) to a stop
f is the coefficient of the road surface (dry asphalt you can use 0.70)

This will give you the speed of the car just before it locked up the brakes.

If you want to determine the time of the vehicle sliding to a stop then use: time = (velocity initial - velocity ending) / a

a = negative acceleration of the vehicle on the road surface

or... a= gf

a = gravity times cof of road (0.70)
a = 32.2 times 0.70 = 22.54

To convert speed to velocity take the miles per hour times 1.47 = velocity in feet per second. (divide velocity by 1.47 to get fps in mph)

In a traffic light scenario never mind the length of the green. What you want to know is the length of time of the yellow light. Now not all yellows are the same BUT generally in my area they are 4 second yellows for a two or four lane roadway. The larger the intersection then the yellows can be longer. Because of perception/reaction times I would be cautious of there being yellows less than four seconds long.

Perception/reaction is generally calculated at an average of 1.5 seconds..sure there are shorter and longer times because people are different but 1.5 is a good average to use.

Systematically first figure a speed from the slide to stop formula. Then make a drawing showing an intersection with a stop line. Without knowing where in the intersection the vehicle stopped, you are going to have to make some assumptions.

One assumption is where would the vehicle have to be to travel at the determined speed, perceive/react and slide to stop ending at the stop line. You are going to have to think and work backwards on the drawing for this.

Then you are going to have to work into this drawing where the car would be based on the instant the light changed to yellow and then for each second of the yellow until it changes to red.

Time/distance calculations in collision reconstructions take a lot of time and paper...have fun with this and it will become a little easier to understand.

I hope this gets you started, I will keep checking back if I can help further.

Casey