Physics proof for traffic ticket

[12markkram34]

So I read about a scientist who wrote a physics proof to prove that he did not run a stop sign, basing his argument on the fact that angular speed of a car moving near a stop sign )as observed by a distant perpendicular observer) peaks shortly before and after the stop, where the observed angular speed is zero. During that brief moment that the speed is zero, another car was blocking the sight of the officer. It's probably easier to understand if you read the actual proof.

The proof is here: http://arxiv.org/pdf/1204.0162v1.pdf

So I understand everything up to part IV, where he calculates the times that obstruction starts and ends. What I don't understand is why he added the two lengths together for one and subtracted them for the other. I think the problem is that he doesn't really specify where the obstructing car is at a particular time, though it could just be me because I'm not really good at mechanics.

Of course, his overall argument is pretty unrealistic since it contends that acceleration starts immediately after deceleration, but I still want to understand the basis of the "proof."

EDIT: I also see an issue with how he defines where his car is. From his part about speed, we can assume that he is defining x as the distance from his front bumper to the stop line. If that is the case, then it would not make sense to calculate when his front bumper is the sum of the lengths away from the line, since if partial obstruction began when he was at that point (that would make the front bumper of the obstructing car be l1 away from the line), his car would be exposed at the stop line (since the obstructing car does not reach that far). Could it be just that that part of his proof is totally bad?

 

[12markkram34]

Bumping since it's been two days without a response.

 

[A.T.]

What I don't understand is why he added the two lengths together for one and subtracted them for the other.

That makes sense for calculating total and partial obstruction. But I didn't go through his math.

 

[Jasso]

What I don't understand is why he added the two lengths together for one and subtracted them for the other.

His definition of the distance of partial obstruction spans when the front bumper is the same distance from the stop sign as the other car's rear bumper, to when his rear bumper is the same distance as the other car's front bumper.

Assuming the other car is stationary at the stop sign, this is a distance from when the front bumper is at $x_1 = -l_2$ (front bumper is even with the other car's rear bumper) to when the front bumper is at $x_2 = +l_1$ (rear bumper is even with the other car's front bumper). Using $\Delta{x} = x_2 - x_1$ gives $x_p = (+l_1) - (-l_2) = l_1 + l_2$.

His definition of full obstuction occurs when the rear bumper has passed the other car's rear bumper, yet his front bumper has not passed the other car's front bumper. So at the point when his rear bumper is even with the other car's rear bumper, his front bumper has a distance of $l_2 - l_1$ to travel before it goes past.

I think the problem is that he doesn't really specify where the obstructing car is at a particular time, though it could just be me because I'm not really good at mechanics.

He is using small angle approximations. Actually, he uses a lot of simplifying assumptions, approximations, and worst case scenarios, probably for an audience which does not have a thorough background in physics.

 

[PJC01]

I find this approach to proving a traffic ticket to be intriguing. It is not uncommon for scientific principles to be used in legal cases, and in this situation, the individual is using the principles of angular speed and obstruction to argue their case.

From my understanding of the proof, the individual is using the concept of angular speed to show that their car was not in motion when it passed the stop sign. This is based on the fact that the angular speed of a moving object is zero at the point where it changes direction, in this case, the stop sign. By showing that the angular speed of their car was zero at the stop sign, they are arguing that they were not moving and therefore did not run the stop sign.

However, I do see some potential issues with the proof. As you mentioned, there is a lack of specificity in the positioning of the obstructing car and the calculations for when obstruction begins and ends. This could potentially weaken the argument, as it relies heavily on the accuracy of these calculations.

Additionally, as you pointed out, the assumption that acceleration starts immediately after deceleration is not entirely realistic. There are many factors that can affect the time it takes for a car to accelerate, such as road conditions, the weight of the car, and the skill of the driver. Therefore, this part of the argument may not hold up in a real-life situation.

Overall, while the use of physics in this situation is interesting, it may not be the most reliable method for proving a traffic ticket. There are many variables and potential flaws in the calculations that could weaken the argument. It would be best to consult with a legal expert and gather additional evidence to support the case.