Your task: Find the capacity of a traffic light.
The worst case is a line of cars is standing still at the light when it turns green. Cars accelerate. The last car to get through the light is at braking distance from the light when it turns yellow.
Starting from a dead stop and accelerating up to the speed limit, how far will a car travel at time \( t \)?
Some sources for information about car performance: 1, 2
You may need to translate this information into a form suitable for your calculation.
What’s the sensitivity of the result to the various assumptions? How much uncertainty is there in your guesses about the values of variables? What’s the first thing you would collect some data about?