For my engineering class. We haven\'t really covered anything like this so I don

Question

For my engineering class. We haven't really covered anything like this so I don't know what to do.

During rush hour, cars back up when the traffic signal turns red. When cars line up at a traffic signal, assume that they are equally spaced (deltax) and that all the cars are the same length (L). You do not begin to move until the car in front of you begins to move, creating a reaction time (deltat) between the time the car in front begins to move and the time you start moving. To keep things simple, assume that when you start to move, you immediately move at a constant speed (v). If the traffic signal stays green for some time (t_g), how many cars (N) will make it through the light?

Explanation / Answer

Let, N cars make it through the signal

dt is the reaction time

So, effective time for which cars were moving with a speed v

(Tg - N*dt)

so,

Total distance travelled by the last car during the time for which traffic signal was open, d

v*(Tg - N*dt)

Total cars making out

N = d/(L + dx) = V*(Tg - Ndt)/(L + dx)

N = VTg/(L + dx + vdt)

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