Should you slow for that yellow light, or should you go through?
From my gauzy past, I recall the pedantic drivers’ ed instructor harping on this: “A yellow light means CLEAR THE INTERSECTION. It does not mean ‘slow down’. It does not mean ‘speed up’. You have to make that judgement call.” What a dilemma! My teenage male brain said, “Sweet! I can SPEED UP!”, while the rational part of me wondered how the heck was I supposed to know whether to speed up or slow down? Do I just guess? (at the time: yes, as it turns out)
Thirty years later, my son, after taking driver’s ed, told me something very interesting: his instructors told him that the city has strategically painted the solid line, that separates the lanes, before an intersection (pointed out with the arrow in the image above), to help resolve this dilemma. Supposedly, the solid lines are painted a very specific length, based upon the speed limit, and the time for a yellow light. If you are driving the speed limit, and the light turns yellow BEFORE you reach the solid lane line, then you should slow down. If you see the light turn yellow and you are already past the beginning of the solid line, then you should continue on.
Brilliant, right? But I’m skeptical, and that skepticism has nurtured a project idea for a physics class, dealing equations of motion.
You have ∆x = length of lane line, or depending upon the calc, = (length of lane-line + length of intersection + length of car, possibly)
t = time for the yellow light
V0 = speed limit
That should be enough to check the continue on scenario, where a person has just reached the solid line when the light turns yellow, because you can assume that there should be no acceleration in a law-abiding driver. (Yes, big assumption, I know)
If you want to check the slow down scenario, then you’re going to need to know things like average stopping distance for cars at certain speeds, which would allow you to approximate accelerations for the cars…so that you can use some of the equations that have acceleration in them. The kinematics equations require the assumption of constant acceleration, which might be a reasonable first-approximation in this scenario, and would certainly create a great conversation with your students to help reinforce the requirements for those equations.
So many lab and community possibilities! Students can travel to various intersections around the city, and safely measure, along the sidewalk, the length of the solid lane lines. They can carry out calculations. They determine whether the lines are the length promised by this scheme. They present to either city officials, or to local driver’s ed teachers with a map of intersections that DO work, and intersections that don’t.
What if your city hasn’t hatched this sort of scheme? Wouldn’t it be cool to get your city to repaint those lines? Students could still visit intersections and measure, and tell the city that they could add just the right amount of solid line, or take away just the right amount, and there you have it! Physics makes your life safer.