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Every driver will occasionally have to make a quick decision whether or not to stop at a yellow light. His intuition about this has been built up by many tests and some mistakes, but a calculation might reveal some situations where intuition will not help.
For some given light duration and intersection size, what combinations of initial speed and distance require you to stop (or run a red light)? What range of speed and distance would allow you to make it through in time?
Notice that for a certain range of these parameters you can choose either to stop or not. But there is also a range in which you can do neither in time, in which case you may be in a lot of trouble.
Upon approaching an intersection whose light has just turned yellow, you can stop at a maximum negative acceleration, race through at some maximum positive acceleration, or maintain your same speed.
For example, let us consider the following parameters: your car is moving at 20 mph (30 ft/s) when the light tums yellow, the intersection is 30 ft wide, the duration of the yellow light is 2 s, and the maximum acceleration is either +10m/s² (for increasing your speed) or -10 ft/s² (for stopping). Assuming ideal conditions (e.g., that your engine instantly responds to a push on the acceleration pedal), we can calculate the distances to the intersection needed for your three options. In order to race through successfully, you would have to be closer than 50 ft when the yellow appears. To stop successfully, you have to be further away than 45 ft.
Between 45 ft and 50 ft, you have either option.
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Prof. Sérgio Torres