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 (∆x) 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 (∆t) 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).
- a. If the traffic signal stays green for some time (tg), how many cars (N) will make it through the light?
- b. If the light remains green for twice the time, how many more cars will get through the light?
- c. If the speed of each car is doubled when it begins to move, will twice as many cars get through the light? If not, what variable would have to go to zero for this to be true?
- d. For a reaction time of zero and no space between cars, find an expression for the number of cars that will pass through the light. Does this make sense?
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