Estimating Speed and Distance for Traffic Light Troubles

[limitapproaches0]

Your task in this assignment is to estimate how fast you would have to be driving and at what distances from the traffic light you get in trouble. It is clear that if you are very far, then you can always stop, and if you are very close, then you can always pass with the yellow. But there is an in-between region that is problematic.

First, you should recall why this happens. This is the part of an investigation where you identify the main problem and its general features. I suggest that you review your notes of chapter two when we talked about this problem and review the textbook.

Then, you should go into specifics. The answer to the problem depends on how long the yellow light stays on, the maximum forward and backward (breaking) accelerations of the car. In class we just made up some numbers to see how the problem worked, but you should try to get real numbers here. This is a case-study.

So, you should get real data on how long the yellow light lasts on different traffic lights and what the maximum acceleration of cars is (some data on real power output and car masses may help). The size of the intersection also matters, since if you are trying to stop, then you should stop before the intersection and if you are trying to pass, then you must clear the whole intersection. You may also want to consider the driver's reaction time.

Finally, you should worry about the maximum speed of the car. If, in order to pass the intersection, the car must "floor the accelerator", then you should take into account that after reaching its maximum velocity it just moves with constant velocity.

Your final result should be some data specifying:

1. The velocity where you start getting into trouble,
2. The range of distances where you run into trouble,
3. List those results for several types of traffic lights (depending on how long its yellow light lasts), and several types of cars, using standard size of intersection and average reaction time.


yah this is my assignment and i ve been trying for about 2 weeks now and don't understand this

 

[HallsofIvy]

Have you gone to your teacher to ask for help? If you have been given an assignment and after two weeks have absolutely no idea what to do, then something is seriously wrong and your teacher needs to know that!

 

[BobG]

Your task in this assignment is to estimate how fast you would have to be driving and at what distances from the traffic light you get in trouble. It is clear that if you are very far, then you can always stop, and if you are very close, then you can always pass with the yellow. But there is an in-between region that is problematic.
...
Then, you should go into specifics. The answer to the problem depends on how long the yellow light stays on, the maximum forward and backward (breaking) accelerations of the car. In class we just made up some numbers to see how the problem worked, but you should try to get real numbers here. This is a case-study.

So, you should get real data on how long the yellow light lasts on different traffic lights and what the maximum acceleration of cars is (some data on real power output and car masses may help).

Hopefully, you at least understood you needed to gather data and have already spent a little time at intersections timing the yellow lights and determining how the big the intersections are.

That might be the most interesting part. The assignment mentions a lot about 'data' and doing calculations, but I would suspect behavior has a lot to do with results. In other words, if a person knows they'll make it through the yellow light, they're unlikely to speed up enough to give the person behind them time to get through regardless of how much acceleration the person behind has. Doing this on a Monday morning might even be more interesting. I wonder how many times you see coffee splash against the windshield when an 'over-conservative' driver actually stops at a yellow.

If you're real good, you might be able to clock vehicles going through the intersection and determine their average speed. I doubt the speed limit reflects a realistic speed, but it might be the best estimate you can get (The Colorado Front Range has a lot of technically oriented folks - we all think speed limit signs use a logarithmic scale. We also handle yellow lights based on the principle of the Doppler Effect - if you speed up, the light looks greener).

 

[ZapperZ]

Speaking of yellow traffic lights, did you hear about the physics major who, when approaching a yellow traffic light, drove even faster towards it, hoping it'll appear green?

OK, OK... you may put me back into my cage now...

:)

Zz.

 

[SpaceTiger]

Speaking of yellow traffic lights, did you hear about the physics major who, when approaching a yellow traffic light, drove even faster towards it, hoping it'll appear green?

Reminds me of my favorite bumper sticker: "If this sticker is blue, you're driving too fast." The bumper sticker is red, of course.