## Wednesday, April 18, 2012

### Physicist uses math to get out of a traffic ticket

One wonders if he was let off because they agreed with him or because they didn't want to acknowledge they couldn't understand his paper.

It's well worth reading though the mathematics may be a little too high-level for some. So just for fun I'll simplify it a little (or more accurately a lot). There are three conditions that need to apply - the position of the officer; the deceleration and acceleration of the vehicle and a point where the car is no longer visible.

The paper points out that we as humans don't measure linear velocity; we measure angular velocity. The most readily available example of this is parallax which most people will know even if they don't know that's what it's called.

As a passenger of a vehicle travelling at a near constant speed I'm sure most people will notice that objects that are close to them seem to be zipping past at high speed whereas objects in the distance seem to barely change. This is because we measure speed using angles.

Consider two posts set at a distance away from you and travelling past at the same speed. Mark their start and end positions and draw a line between them and yourself.

The gap between the the orange lines is larger than the gap between the red lines despite the actual distance each post has travelled being identical. Because of this we perceive the closer post as having travelled a larger distance than the further post and to have done so in the same time. Our brains know that speed equals distance divided by time. The closer posts must therefore be moving faster than the further posts.

What this means that as an object moves towards us we perceive its speed to be increasing even if it isn't. In this instance the car is moving towards the officer and they would therefore perceive it as getting faster.

Onto the second condition deceleration and acceleration. As just stated a car travelling at a constant speed would appear to be getting faster as it approached a viewer; but what if the car decelerated? The car itself is going slower, but from the observer's point of view it's simply not going any faster. From their point of view the car is now travelling at a constant speed.

This leads to the third condition a point where the vehicle can't be seen. Our car is decelerating as it approaches the STOP sign, but from the observer's point of view it's travelling at a constant speed. As it draws level and stops the observer's view is obscured by another vehicle. The stopped car then accelerates away.

The reverse situation now occurs in that the car is moving away and will therefore appear to be travelling slower, but it is accelerating and is therefore perceived at travelling at a constant speed.

Put the whole package together and from the observer's point of view the vehicle never appeared to alter its speed and thus could never have stopped at the sign as it was supposed to.