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