No the driver did not speed up

You ever wonder why when you miss a yellow light it always looks like the other driver has sped up? Or when you are trying to merge in it looks like the other drivers are matching speed to just keep you from merging and heading on your merry way.

Well here is some math to help with some of it.  The driver in front of you is Car X while you are in Car Y as you slow down since the light has changed your Car Y’s speed is on a downward curve and though Car X’s speed is at a constant it only appears to be at an upward curve when in comparison to your own downward curve in Speed.  So the the perception is tricked into believe something is happening when it is in fact not.

So first Car X and Car Y have the same constant speed.


Now when you start to slow down you Car Y has a speed shown in this formula.


So while car X still has a constant speed (velocity)  your car is on a downward slope in speed which can be a straight line or a curve depending on whether your speed is constant. Which in the end makes it look like the other car is speeding up as your reach the stationary position.

Math Junkies please comment and see if you can clear up the math a bit more as it is 2 am when I am writing this and well it is a fun little physics problem dealing with an object in motion and another approaching a state of rest.

by Jin Okubo

9 thoughts on “No the driver did not speed up

  1. I can’t comment on the math, but I have always maintained that driving is for people who are good at math. You’re measuring the vectors and relative speed of all the vehicles around you while making decisions on whether to brake or accelerate or stay the same. In your example, you are looking at why something appears to be happening when it is something else.

    Or, the idea of going around another vehicle. When you have vehicles that are going the same or close to the same speed, it takes ages to go around. Vehicles with disparate speeds, on the other hand, the faster one rapidly passes the slower one and there’s less time in proximate vicinity, and therefore, IMO, less time for something bad to happen.

    Changing lanes is another one – it’s tricky and I see a lot of people do it wrong. You try to hit the gaps in the non-moving traffic to change lanes, and it happens in waves.

    There’s your interesting math- look at the theory of heavy traffic and why it moves in waves. There’s a ripple of open space that flows back through heavy traffic, so that cars are constantly moving forward, then stopped, moving forward, then stopped. Looked at overhead, the movement is in waves. Ideally, to even out traffic, if people drove at 20 kph no matter what (if they have open space in front of them), that would even things out as it’s a time/distance/space problem.

    Liked by 1 person

      1. I’ve seen some fantastic simulators for certain traffic conditions, which are fascinating studies for engineers in what is essentially the mathematics of particle flow. Particles that have certain properties, average reaction times, and interact in a certain way based on the pipes or tubes they are channeled through… See this site, which is a graphical representation of exactly those factors:
        I love this stuff. Honestly. It’s a character flaw.


  2. It all goes back to what Albert was referring to when he spoke of relativity, i.e. it’s all relative. You’re attempting to fit the physical phenomenon, describing the mathematical expression of what the car is doing, into what the mind/brain does when it observes the separate motions; but, often, the mind can overcome the math, and the perception, if practiced. Think about sitting in a train, with another train next to you…. if one moves, can you tell which one? It often appears the other train is moving, when it is our own… It’s a variation of the two car situation described here; we perceive motion, when we are

    It’s all relative, to where you are observing the phenomenon, and, your own perceptive ability,… Your vision and mind do the math unconsciously, naturally; that’s how we learn to drive, to fly a plane, etc. without actually learning the math involved in doing it…. And, as your math demonstrates, the physical reality doesn’t always match our perceptions of it…

    gigoid, the dubious…

    Liked by 1 person

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