The Traffic Problem

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    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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    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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    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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    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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    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.