The Traffic Problem
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Transcript of The Traffic Problem
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7/31/2019 The Traffic Problem
1/5
Eamon BarkhordarianMalik GillKabir Gill
11/1/2011Physics APB
The Traffic Problem
It was a beautiful, lazy Sunday afternoon. The calm breeze was just barely sweeping the
streets. The sun was glistening. The birds were chirping with utmost passion, and there was a
calm, serene feeling that was blessing the entire community. Everyone was driving very slowly.
But Tim was late for Sunday school. As he hurried to Gunn, too much was on his mind.
Cars zoomed by him as he panted his way to school.
He was almost there. As he approached the T-intersection of Gunn High School to make
a right, the light turned red. It didnt matter. Tim chose to break the law and cross the red light totry and make it to school on time. Yet, he didnt see the car pulling out of the parking lot and
crashed head first into the vehicle.
He was out cold, and the car he crashed into had a massive dent on its side with the shape
of a bike. Good job Tim. Great Job. Luckily, Tims good friend Harley Davidson was there to
take him to the hospital.
Investigators later visited the scene and wanted to decide if Tim had a reasonable amount of
time to turn on the intersection, or if he simply was a crappy biker. To see, the investigators
decided to find out how many vehicles could pass through intersection during a green-yellow-
red interval.
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7/31/2019 The Traffic Problem
2/5
Eamon BarkhordarianMalik GillKabir Gill
11/1/2011Physics APB
Our rules:
2 meter long motorbike
1 meter distance between each bike 2 lanes
20 meter long intersection. 20 meter wide intersection.
30 second light: 25 seconds green, 5 seconds yellow (25 seconds red)
Speed limit 60 mph
Bikes accelerate at 2 m/s
2 second reaction time
Bikes cross the intersection once the front of the bike crosses the first line.
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7/31/2019 The Traffic Problem
3/5
Eamon BarkhordarianMalik GillKabir Gill
11/1/2011Physics APB
Written Description
The intersection Tim got hit on was a T intersection, but now because of the accident, the
split side of the T was cut off, leaving a straight, two lane road. (See picture if confused). The
intersection itself is a square that is 20 meters by 20 meters. The road is two-laned and filled with
motorcyclists, who all use the same brand of motorcycle that is 2 meters long. The front of the
first bike of each lane is exactly on the line of the intersection, but not in the intersection. Every
bike behind the first bike is one meter apart from each other. Also, the front 2 bikers have instant
reaction times when the light turns green, and every biker behind them has a two second reaction
time from the biker in front of them. Each bike accelerates at 2 meters/second. The stoplights are
green for exactly 25 seconds, yellow for 5 seconds, and then red for 20 seconds (30 second
length). To cross the intersection, the front of a motorbike has to have crossed the line of the
intersection, and then we assumed that it would be out of the intersection in time.
How we came up with our rules
We came up with our measurements by using common sense rather than experimentation.
We figured that the average bike on a Lazy Sunday could accelerate at 2 meters/second, so we
implemented it into our problem. The green light lasts long so we could have a realistic amount
of cars go through the intersection. The two second reaction time is also what we figured our
own reaction times would be, because people are not always looking at the car in front of them
(sometimes they are changing the radio stations or putting on makeup, etc.).
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7/31/2019 The Traffic Problem
4/5
Eamon BarkhordarianMalik GillKabir Gill
11/1/2011Physics APB
Equations Used
First we made an equation to find the distance to the intersection for each bike. We first
made a table of the values for the different cars considering the length of each bike and the
distance between bikes.
X (# of bikes from intersection) Y (distance from intersection)
1 0
2 3
3 6
4 9
We then created the equation from the table above: position (meters from intersection)
= 3(X-1) where x is the number of the bikes from the intersection.
Then we calculated the time it would take for each bike to make it to the intersection
using the equation for position which is x= at2
+ Vot + Xo. Since our acceleration was
2, our initial velocity was 0, and our initial position was zero, we found that time it would
take for each bike to make it to the intersection would always be the square root of the
distance equation. As a result, we got :
Time to intersection (seconds) = 3(x-1) where x is the number of the bikes from the
intersection.
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7/31/2019 The Traffic Problem
5/5
Eamon BarkhordarianMalik GillKabir Gill
11/1/2011Physics APB
Now we have to account for the reaction time that each driver would have (2 seconds).
So at the end of the equation we add 2(x-1) where x is the number of the bikes from the
intersection so that the final equation is:
Time to intersection (seconds) = (3(x-1) + 2(x-1) where x is the number of bikes
from the intersection.
Because the intersection lasts 30 seconds (25 seconds green and 5 seconds yellow), we
plugged in 30 seconds for time and solved for the amount of cars.
30 = (3(x-1)) + 2(x-1). We brought 30 to the other side of the equation and calculated
the zero for the equation 0=(3(x-1) + 2(x-1) - 30.
Our answer was 13 cars from one lane, but because there are two lanes, we multiply this
by two and find that 26 cars will make it through the intersection each cycle.