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Math Help - Optimisation - Modelling question

  1. #1
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    Aug 2011
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    Optimisation - Modelling question - Solved

    Good evening.

    I have been issued a number of questions in preparation for upcoming assessment tasks and have found difficulties with a particular modelling question. I apologise for the length of the question.

    My question is how do I begin the question. What would be the correct way to approach it. I am fairly confident with most of working but the initial step is where i struggle.

    Thank you in advance for assistance offered.

    The transport department have come to you as there was an error with the table they supplied you. A new table is given below. Recalculate the formula for traffic flow and advise of the new safe speed at which to travel.

    Remember: The transport engineers produced the given formula by using the following list of assumptions.
    Assumptions:
    1. All cars are approximately the same length (average = 4.2m).
    2. In dense, uniform traffic flow, all cars maintain the same “safe distance” apart.
    3. This “safe distance” is the stopping distance required for a car travelling at V km/h. This distance is composed of two parts – (a) Reaction Distance, the distance the car travels as the driver reacts to the situation and applies the brake, and (b) Braking Distance, the distance the car travels once the brake has been applied.
    4. The NEW “safe distance” can be reliably obtained from the table below based on the Ministry of Transportation Code used in England.
    Velocity (km/h)

    Reaction Distance (m)

    Braking Distance (m)

    10

    2.23

    0.5

    20

    4.86

    2.0

    30

    7.89

    4.5

    40

    11.32

    8.0

    50

    15.15

    12.5

    60

    19.38

    18.0

    70

    24.01

    24.5

    80

    29.04

    32.0

    90

    34.47

    40.5

    100

    40.30

    50.0

    5. Number. of cars/second = [IMG]file:///C:/Users/Joel/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png[/IMG]
    Last edited by CaptainBlack; August 8th 2011 at 02:02 PM.
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