The Problem During rush hour, cars back up when the traffic signal turns red. As

Question

The Problem During rush hour, cars back up when the traffic signal turns red. Assume: cars lined up at a traffic signal, are equally spaced (Ax) and the same length (L); you do not begin to move until the car in front of you begins to move, creating a reaction time (At) between the time the car in front begins to move and the time you start moving; and when you start to move, you immediately move at a constant speed (V). If the traffic signal stays green for some time (tg), how many cars (N) will make it through the light? What you need to do (Instructions) Use SOLVEM to analyse this problem, and create an expression that can be used to solve a specific question about the situation

Explanation / Answer

Objective : to find out how many cars made it through the green light in tg time
Varaible : time taken by each car to cross the green signal. The distance of each car from the signal. Wait time of each car before it can start.

Equations and manipulations:

    Assuming n number of cars passed by.Time taken by Nth car to cross must be equal to tg
    Time taken by nth car = wait time + time taken to each the signal
    Time taken by nth car = (n-1)d(r) + ((n-1)(L+d(x)))/v  

                            d(r) - delta reaction time
                             d(x) - space between cars
                             L - Length of the car
                             v = velocity of the car.

    = (n-1)d(r) + ((n-1)(L+d(x)))/v = tg
        (n-1) (d(r) + (L+d(x))/v) = tg
         n = tg/(d(r) + (L+d(x))/v) + 1                      

If d(r) becomes zero and velocity is doubled , we can have twice the car passing through.      
  

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