## Tuesday, April 10, 2012

### Physicist Uses Math to Beat Traffic Ticket

Here's a practical application for your physics education: using math to successfully beat a traffic ticket in court. Dmitri Krioukov, a physicist based at the University of California San Diego, did just that to avoid paying a fee for (purportedly) running a stop sign.

Krioukov not only proved his innocence, but he also posted a paper detailing his argument online on the arXiv server. The succinct abstract for his paper certainly distinguishes itself from other research papers:
"A way to fight your traffic tickets. The paper was awarded a special prize of \$400 that the author did not have to pay to the state of California."

After thinking Krioukov ran through a stop sign, a nearby police officer pulled him over and issued him a citation. According to Krioukov's paper, however, three physical phenomena combined at just the right time and misled the officer.

When Krioukov drove toward the stop sign the police officer was approximating Krioukov's angular velocity instead of his linear velocity. This happens when we try to estimate the speed of a passing object, and the effect is more pronounced for faster objects.

Trains, for instance, appear to be moving very slowly when they are far away, but they speed past when they finally reach us. Despite these two different observations at different distances, the train maintains a roughly constant velocity throughout its trip.

In Krioukov's case, the police cruiser was situated about 100 feet away from a perpendicular intersection with a stop sign. Consequently, a car approaching the intersection with constant linear velocity will rapidly increase in angular velocity from the police officer's perspective.

Similarly, if a car approaches the stop sign with constant velocity but brakes quickly before reaching the sign, the angular velocity will rapidly increase before stopping momentarily. To illustrate this point, Krioukov created two graphs: one for the case of constant linear velocity through a stop sign (illegal) and another for a quick stop at the sign before accelerating back up to speed (legal).

If you look at the graph on the right, you'll notice three lines with different colors, and each line corresponds to a different deceleration at the stop sign. The blue line with the biggest spikes represents a 10 m/s^2 deceleration -- about the highest deceleration for the kind of car he was driving.

This line mimics what actually happened best according to Krioukov because he had a terrible cold that day, and one sneaky sneeze caused him to slam on the brakes hard as he approached the stop sign.

The crux of Krioukov's argument is that this rapid, legal deceleration can appear very similar to the case described in the graph on the left. But the left graph actually represents a car cruising through the stop sign at a constant velocity exceeding 20 miles per hour. So surely an officer would still be able to tell the difference, right?

Not when another car partially obstructs his view, according to Krioukov. When another car partially blocked the officer's view of Krioukov's car momentarily, the officer could have missed the brief yet crucial timing of his stop. At least, that's Krioukov's version of the case.

Either way, his argument appeared to work: "The judge was convinced, and the officer was convinced as well," Krioukov told PhysicsCentral.

This physical description swayed the judge, or maybe she was simply impressed by the sheer dedication Krioukov put into avoiding this ticket.

You can peruse the paper here if you want to devise your own plan to get out of traffic tickets. Leniency in court, however, is not nearly as reliable as mathematical proofs.

Mathematical figures courtesy Dmitri Krioukov. Top stop sign image courtesy Infrogmation via Wikimedia commons.

1. Nice. The only flaw I noticed is the date of the paper, April 1st. Apparently, Physics Central hasn't noticed this flaw, so it didn't diminish the scientific credibility of the paper. ;-)

1. It says April 10th not April 1st.

2. The story is the 10th, the paper is dated the 1st.

2. You'd have to quickly accelerate after the stop to match the speed you should have been going after the stop sign. The sneeze explains the quick stop, but what explains the quick start?

3. As the previous comment points out, what explains the quick start?

The title is right: physicist uses math to lay snow job on traffic court—and so doing beats traffic ticket.

4. Lubos: I noticed that the paper was posted on April Fool's Day, so it definitely seemed a little fishy. When I spoke with Krioukov over the phone, however, he seemed to provide a few details about the court case that made the story sound quite plausible.

As far as the quick start is concerned, that may very well be the flaw that Krioukov alluded to. The Toyota Yaris that Krioukov was driving definitely could not accelerate as quickly as its maximum deceleration.

Without assuming the same acceleration and deceleration, the "legal" and "illegal" graphs would not look nearly as similar.

Nice job Anonymous and Gustavo for noticing this.

5. When his Toyota was momentarily at rest, D.K's ability to look to his right would have been blocked by the Subaru. He should not have proceeded immediately to accelerate away from the stop sign without being able to determine if traffic was coming from the right. -Jeff Melmed (jmelmed@emcc.edu)

6. Anyone would be impressed with the dedication. Now that it worked, and saved \$400, it will remain a talking point. Long live Pseudoscience!

7. Physicists don't say "deceleration." Both are acceleration.

1. Yeah we do. We do it all the time. Myths about what physicists say are propagated by highschool teachers with too much zealotry for the field. Admirable, but pedantic and irrelevent. I'm more concerned with the way that the universe works. If someone adds a prefix 'de' to replace the 'a' to tell me the sign is negative compared to it's current velocity, fine by me.

8. I think the flaw is actually that he claims the vehicle stopped while obstructed by the Subaru. He claims the vehicle stopped in a distance of 16 feet. However, that is predicated on the concept that he stopped while the vehicle was fully obstructed by the Subaru. Otherwise, the officer would have been able to judge the speed of the Yaris by watching the speed of his rear bumper. The Subaru was 189 inches long, the Yaris was 150 inches long, and therefore the rear of the vehicle would be visible until the Yaris was 39 inches from the stop sign. He supposedly stopped in 39 inches instead of the 16 feet he claimed.

9. I do not understand how ha find xp and xf. Is the subaru mobbing or not? And what is it's acceleration?

10. Sorry i mean "he" and "moving" not mobbing

11. And where is the subaru when the first car reach it?

12. Oh now i understand There is an error in figure 4

13. OPEN CHALLENGE

The article ‘On the Electrodynamics of Moving Bodies’ by Albert Einstein is based on trickeries is proved beyond any doubt whatsoever in the articles (1). ‘Experimental & Theoretical Evidences of Fallacy of Space-time Concept and Actual State of Existence of the Physical Universe’ published in the peer-reviewed journal namely Indian Journal of Science & Technology (March 2012 issue) available on www.indjst.org (2) ‘On the Electrodynamics of Moving Bodies By Albert Einstein is Based on Trickeries’ (Open letter to Professors, Teachers, Researchers and Students of Physics) published in peer-reviewed journal Elixir Online Journal (February 2012 issue) available on www.elixirjournal.org. The Voigt transformation was simply a mathematical possibility which was changed by Lorentz by introducing the Lorentz factor but the Lorentz factor is simply a manipulation. Thus nature and forces in nature were trivialized and made subservient to mathematics in the theories of relativity, Big Bang Theory, Space-time concept and in all physical sciences which are directly or indirectly based on the ‘On the Electrodynamics of Moving Bodies’. It is unfortunate for humanity that exposing these trickeries took more than one hundred years.

I openly challenge all the professors, researchers & teachers of physics/philosophy of physics to come forward & show me where I am wrong or else they have to accept that they are teaching incorrect physics based on ‘trickeries’.

My challenge may not be treated as a publicity stunt but I sincerely wish that truth should prevail on this planet and am expecting identical response from all truth loving people/intellectuals. I do understand that it is hard for mainstream physicists to reconcile with the alternative philosophy; though actual and factual; as almost all the living physicists and researchers are borne, brought up and taught physics which is fundamentally incorrect. Their livelihood is based on the physics which has been adopted as the result of fraud, but these material interests should never be a stumbling block to acknowledge the reality, which to my understanding is the essence of scientific thinking and honest living for the betterment of entire human society.

I have not an iota of doubt that sooner or later the truth will prevail, but it would be in the interest of humanity that ‘truth’ is accepted now so that humanity comes out of clutches of materialism which in itself is naked atheism.

(M.Sc. Physics)
(M.Sc. Forestry)

1. so what is your point? Allah made it all.Right? So why are you listing your degrees? Why did you study Physics, if you have the answers.

2. Here is the flaw: linear velocity = angular velocity x radius. Radius in this case is the distance from the officer to the stop sign, which is a constant. So, if the linear velocity is not zero, then the angular velocity is not either. Therefore, the physicist could not have stopped at the stop sign because the officer, even at an angle did not see that his car has stopped despise his view was partially block the the Subaru. The equation above shows that the officer was correct.

3. Earthy degrees do not deny accepting Allah who is beyond the laws of physics. The listing of degrees may be a good case to show, if you have similar degree, then earthy scale is the same. The question comes, what is for the hereafter? If nothing, both fine. No degree, nothing. But, believing in Allah and being righteous do not hamper holding the degree and mentioning it.

4. (Apologies, for further encouraging something completely off-topic...)
I can tell you where you're wrong: (1) By placing the burden of proof for YOUR argument on those you're challenging; (2) Presenting the false dichotomy that if nobody "shows you where you are wrong", they must be willfully teaching incorrectly.

(P.S. - logic beats Allah: Way to bring some bigotry/religion in on it. Good work.)

5. The field you are referring to has been tested to death. First off, Maxwell's equations are lorentz invariant to begin with. Each term was painstakingly constructed from experiment, all of which you can reproduce from scratch if you like. Once they are built, the model is intrinsically invariant under the Lorentz transform. The point is that reality told us this, it wasn't cooked into the equations.

Now applying this transform to relativity was indeed a theoretical jump. However, we have tested that formalism better than any other theory in history. That QED predicts the cross sections for electron scattering to something like 13 digits says that we have it right. Every conceivable test of this theory that's been performed has sided with it.

Every competent physist understood the origin of the lorentz transform in relativity. It isn't trickery, you apparently didn't pay attention in those classes you took to get your "MS.C in physics". It's a model built like all models. It's merit is entirely in it's ability to predict reality. How it was developed is besides the point, although the idea that there could be trickery in such development is beyond stupid, it illustrates a completely missunderstanding of both mathamatics, and physics. Frankly, science as well.

If you don't agree with the theory, that's your business. I disaggree with lots of theories. But I have evidence for it. That's how science works. If you want it to change, you provide evidence for it. We've provided evidence that special relativity and the quantum mechanics which now relies on it works excellently. We have 70 years of papers supporting this, including literally as much data as the web occupied just a few years ago. If you want to make a dent in it, you need to provide experimental proof otherwise. IF you did, we'd listen and adjust our theories. That's how science works.

14. The flaw is theres no ticket or dismissal to prove whether this is bullshit or not.

15. The Subaru blew through the stop sign... why didn't the cop stop him?

"I openly challenge all the professors, researchers & teachers of physics/philosophy of physics to come forward & show me where I am wrong or else they have to accept that they are teaching incorrect physics based on ‘trickeries’."

It is a shame that 100 years of "trickery" has continued. The bottom line is that there is a preferred frame as I've shown in my diagram at http://www.freeimagehosting.net/47g8k

I also challenge anybody to show how the light can reach the x and z receivers in the diagram in the same amount of time in the cube frame. As per the second postulate of SR, the speed of light will be measured to be c in all frames of reference, which I have clearly shown as false. It is IMPOSSIBLE for the speed of light to be measured as c in the cube frame from the source to the x receiver and the source to the z receiver.

1. Time dilation and length contraction. You don't take into account relativistic effects of the cubes motion.

2. That's just the point, that there is no time dilation or length contraction. The speed of light is always 299,792,458 m/s in my diagram, the length in the cube frame from the source to the receivers is .5 light-seconds, and the light is emitted from the source and yet... it is IMPOSSIBLE for the light sphere to contact each receiver in the same amount of time.

17. The physicists ignores inertia!!

18. Anything quick (start or stop) is incompatible with a Yaris!

19. Sweeny BuggtussleApril 13, 2012 at 2:01 PM

What are the maximum actual negative and positive accelerations of a Toyota Yaris that could be made, and could that fit into 39 inches one way or the other. How fast was the car going when it slowed, how long was it at a total and complete stop and not moving at all, how quickly did it get back to moving speed. Does 39" cover of that to an observer . Even at the 17.9 MPH in figure 5. Or the 22.36 MPH and 32.81 feet in figure 2. How many feet can you fit into a shoe, and how much confusing gibberish does it take before you give up and dismiss a notional traffic case? Hah, yeah, yeah

20. Bottom line is no way the lawn mower engine that comes in a Toyota Yaris could positively accelerate at the same 22.36 mph/s that it negatively accelerates at.

21. It's pretty simple actually. The entire analysis is based on the premise that the cars are in parallel to each other and the officer is 100ft away from the roads.

When in fact in the description of the problem, it said the intersection is perpendicular. Therefore the entire analysis is invalid because the cars cannot be parallel.

22. Isn't there supposed to be a 3-count at the stop sign before continuing? This means regardless of whether he stopped quickly or not at all, he is still in violation of the full stop. Brake dive is not a full stop, even if the wheels are locked.

23. ^ your just flat out wrong.

24. Reviewing Prof. Krioukov's paper, I believe the flaw begins in Eq. 8: x(t) = v0*t + 0.5*a0*t^2. This implies that omega(0) = v0 / r0, NOT zero. So, in fact, O's perception in FIG 5. may be correct! and the good Prof. got away with it! Well done Prof. Krioukov!!

25. Why would the author mention the length of the vehicles if it didn't have something to do with the Subaru's ability to block the Toyota from the officer at the stop sign? Given this, it must have something to do with stopping distance, also. I think Brady has discovered a flaw.

26. Its obvious that pigs lie. Was the pig even there to 'witness' the 'offense'?

27. It's not constant deccel./accel.. The kinematic equation on the first page is irrelevant.

28. I concluded that no matter how cunning a physicist is at battling a ticket in court, the real objective was to save money, since he obviously can't afford anything better than a Yaris. I would look closer...he probably got a ticket because for owning a Yaris, and the stop-sign was just probable cause.

29. the genius of geniuses geniui: the solution to all yer problems is in the date: April 1. no foolin'

30. He assumes the that S angle is 90 degrees? I didn't read the paper as it won't make sense to me anyways but the article was entertaining. I think he just got a kick out of the whole thing.

31. The time is off. Notice a full 2-3 seconds between maximum angular velocity in fig 3. Meaning the other car would have had to block him for that long until the angular velocities roughly matched up again. Also, the cop was 100 ft away, not 32 feet away. The further away you are from an object moving perpendicular to you, the better the match between linear and angular velocity (cosine approaches 1).

32. His flaw? None of those equations accounted for the brief temporal flux that was established as the capacitor experienced a "hiccup" and the Yaris was instantaneously thrown forward milliseconds through time and space, having completely passed the intended space and time for the stop.So the professor got away with it due to a faulty flux capacitor!!

33. I believe the flaw is that roads with two through lanes in one direction (two vehicles in two lanes in the same direction is what is used in the argument) do not have stop "signs", they are regulated with stop "lights".

1. Not sure where you live, but we have plenty of 4-lane roads (two lanes in each direction), that are regulated by stop signs...not lights.

34. The argument assumes that the car accelerates to its pre-deceleration speed in the same amount of time and distance as the original rapid stop. This ignores the difference between static and rolling friction and the time required to overcome inertia once stopped. Because static friction is greater than rolling friction, and becasue inertia must be overcome before the stopped car can begin to move, a car cannot accelerate to its pre-stopping speed in the same amount of time and distance as it decelerated when the brakes were suddenly applied with maximum force, even assuming that the tires do not "skid-and-squeal" while stopping and that they do not "peel-and squeal" while accelerating.

35. According to the graph on the right, there is no time passing while the car is stopped. A broad definition of a stopped car is a car in which there is no movement made over a change in time. There for the integral of the acceration will equal zerro. This graph isn't continuos and doesn't have an integral at t=0.

36. Shouldn't car 2 be headed in the opposite direction? Otherwise it should have stopped at the same stop sign, blocking the view. If it cam from the opposite direction, it could obstruct the view of the officer without stopping.

37. His argument does not account for the angular displacement. Assuming a straight road, O's perception would observe much more than pi radians (180 degrees) of angular displacement. Think the area under the dotted red line v area under the red line.

38. Wow. You retards are way-overanalyzing this to find the "flaw". The flaw is readily apparent, easily verified by common sense, and NOT based in high-level math. The flaw is that he says he had a cold and therefore braked very hard very close to the stop sign. WHY WAS HE GOING SO FAST, SO NEAR THE STOP SIGN? A normal person would start to slow down earlier, like in the red and green graphs. Did he somehow predict the future that he would sneeze and brake so hard? No. Obviously he intended to just cruise through. So the "sneeze" argument is logically invalid. His argument would have been valid if he had simply said "I just wanted to brake really hard and accelerate really hard because that is my driving style". But sneezing implies an accidental fast brake, which DOESN'T EXPLAIN WHY HE DIDN'T SLOW DOWN EARLIER.

1. People who use words like over-analyzing and no-brainer are the true retards. He doesn't have to EXPLAIN WHY HE DIDN'T SLOW DOWN EARLIER. The question is irrelevant. What if he is a hard braker with a lead foot? Then in either case he would brake hard from predisposition or from a sneeze. What difference does it make what he assigns as the cause? I must emphasize again that you are retarded.

39. The flaw is that he's driving a Yaris.

40. I just recall what a doctor told me once when I started out as an x-ray tech: the angle of the dangle is equal to the square of the hypotenuse of the crack......I think not only would the professor get out of the ticket, he would not have given the judge a headache.

41. I won't give away his mistake, so that others may have the joy of discovery. I will say that it is the same mistake that many of my students make; perhaps the author also has a small case of dyslexia?

42. He did not mention whether the other car was moving or not.
Also, what is the distance between the two cars?
These two factors might change the obstruction time.

43. Apr 13, 2012 01:31 PM has it right.

Krioukov says his car is stopped for an instant. With no car blocking the view, a hummingbird would think he took the stop sign.

And if he were stopped for more than an instant, it would take a very long, slow moving car obstructing the view to make it appear as if he failed to stop.

44. One more hint: it has something to do with the Mars Climate Orbiter.

45. Actually, it looks like his mistake is just a typo, for his times are correct. When converting inches to meters, the distance should read 8.61 m rather than 8.16 m. The author used the correct value of 8.61 m in his equations, it appears.

46. Trucker said.....April 13, 2012 at 8:55 PM

The Yaris is taller than the Outback, so the Cop never lost sight of the roof of the car!! Trucker said

47. The flaw is that the other car ran the stop sign as well.

48. the flaw is he's using a distorted notion of angular velocity. Eq. 3 in the paper applies to rotation about a fixed axis, and this is clearly not the case in the example. The equation can only be applied if the police officer maintains a constant distance from the car. Moreover, the assertion at equation 4 only applies to the special case of t= some specific value such that v*t gives enough distance from point c to make a right angle with line OS. Eq 4 should be replaced with (if we label line CS a constant distance R) tan(a)=(R-x(t))/r, then you're left differentiating arctan of that... which I've had way too much whiskey to do right now. -Brian

49. to amend my previous point, Eq.3 in the paper can be applied to the problem, but it cannot be used to measure the angular velocity of the car... as the car is not rotating. Rather, it can be used to measure the angular velocity of the imaginary line OC, which is exactly what is being done in this paper. Basically he provided us with a way to measure the angular velocity of the officers head, if his eyes were to remain fixed on the car. Eq. 4, is definitely still wrong though-Brian

50. Flaw 1: He did not come to a complete stop for 3 seconds

Flaw 2: Either he did not know this rule or he tried to defend himself knowingly

Flaw 3: Now that he claims to know for himself of the flaw in his argument, it amounts to deliberately misguiding an honorable court of law which amounts to contempt of court, to the least of offence

Flaw 4: By publishing his paper, he has abused the valuable time of the readers and the bandwidth of the internet

Decision 1:
a) I plan to sue him for the time he has wasted of all concerned,
b) for trying to misguide the public, and
c) for mocking the judiciary of US

51. The angle of the dangle is directly proportionate to the stroke of the poke which in turn determines the heat of the meat.

52. there is no calculation or even an estimate as to the time the other car blocked the view. If the time the view was blocked exceeded the feet per second the defendant's car was moving (at 25 miles per hour the car goes 38 feet per second) the car of the defendant was not blocked for more than a split second, less than 1/2 second unless the blocking car was a extremely long car such as a limousine and even then, the blocking if defendant's car was blocked by such a car, would not at 25 miles an hour be blocked in view for more than 1/2 second.

53. I used Google Street View to see the stop sign in question. The stop sign clearly has a white border around it which, as everyone should know, makes it an optional stop sign. So long as you watch out for errant texting pedestrians, you may perform a "rolling stop" at any speed through these stop signs.

54. Another example of book smart and practical application poor...I used to manage the wood and metal shop while working my way through MIT...the most dangerous times in the shop were during the professors' personal time they spent mangling perfectly innnocent pieces of wood and metal, not to mention the machinery and my nerves.

Case in point, anyone driving a Yaris who "punches it" is going to more likely suffer a broken hand, not an acceleration approaching 10 m/s2--so all the discussion in the world about time dilation factors and length of the vehicle passing aren't going to block the officer's view long enough for the "illusion" to hold. But hey, in theory it worked, so the dweeb considers he "won".

I did continue my studies, and valued the staff with practical knowledge...now close the book (or browser) folks and live.

55. answer (beside it probably being an april fools joke) is that both cars ran the stop sign with the subaru turning onto a side street/driveway/etc. prior to the officer reaching the road and observing where he/she went. he then instead pulled over the yaris. his argument is "correct" if they passed the stop sign at the same time in theory, but common sense should say that both blew the stop sign. \$400 is ridiculous though (although i doubt that's the real fine)

56. "Book smart and practical application poor." Some years ago I was showing a physicist friend from MIT (you know who you are Dr.) around a steam injection project in a California oilfield. He was fascinated, coming up with all sorts of questions about the dynamics of the process. The boilers were so hot that is was difficult to even stand near them for more than a short period. During one of those short periods he decided take a load off his feet, placing his hand directly on the boiler plenum and leaning against it. If there was ever an infinitely short period of rest, that was it.

57. The flaw is that a Toyota Yaris can not accelerate nearly as quickly as it can decelerate. This would significantly increase the time required to resume initial speed and thus be apparent to the Officer.

58. He claims in his model, 'his car decelerated at - 10 m/s^2 and, instantaneously, accelerated to + 10 m/s^2 at t = 0'.

No known mechanical system is capable of achieving such an instantaneous jump without a tail-off period. If a tail-off period is introduced he would have ended up paying the ticket. So, he obfuscates the vision of the judge by his ability to profess physics, or the judge felt it was more economical to dismiss the case than spend time on it.

As a trivial matter of fact, his model is crude and over-simplistic to contemplate any error-analysis of measurement uncertainties.

Here are some links of interest:
http://www.edhat.com/html/california_stop.html
Our scientific analysis determined there to be 3 distinct stages that occur during a stop at a stop sign: braking, unbraking, and accelerating. For a full stop to occur, unbraking cannot be commenced until the vehicle has come to rest. Be aware, some backward motion will occur when the shocks release the momentum they absorbed at the moment the tires ceased to rotate and the car body continued forward.

If unbraking occurs before the car comes to rest, the car will continue to lurch forward until the accelerator is activated. Some natural delay occurs as the right foot moves between pedals. However, in some instances, drivers purposefully postpone acceleration until they have fully ascertained that it is safe to move forward. In fact, the time between braking and accelerating is when most drivers determine whether or not to yield the right-of-way to another vehicle. In other words, they are already ‘California Stopping’ before any driving decision has been made. Once accelerating has been commenced, the entire stopping process is terminated.

http://www.istockanalyst.com/article/viewiStockNews/articleid/4548425

"A driver running a red light, whether they are traveling straight or turning right, makes a very dangerous traffic movement that endangers the nearby motoring public, bicyclists and pedestrians," Schwarzenegger wrote in his veto. "Modifying existing law to make red-light violations from a right turn less egregious sends the wrong message to the public that California is tolerant of these types of offenses."

The traffic tickets have been piling up in the Peninsula and other places where red light cameras snap pictures of violators. The Legislature and some motorists have complained that the punishment does not fit the crime and wanted the penalty lowered to \$219, the same fine slapped on drivers who roll through stop signs.

But police groups around the state said the bill would only encourage drivers to speed through right turns without checking if the path is clear.

"There are few things more dangerous than the California stop," said San Mateo Police Chief Susan Manheimer, president of the California Police Chiefs Association. "Through punitive measures, i.e. fines, we have been able to change behavior."

http://www.ehow.com/facts_5016899_california-line-law-stop-signs.html

According to Vehicle Code 22450, "The driver of any vehicle approaching a stop sign at the entrance to, or within, an intersection, or railroad grade crossing shall stop at a limit line, if marked, otherwise before entering the crosswalk on the near side of the intersection. If there is no limit line or crosswalk, the driver shall stop at the entrance to the intersecting roadway or railroad grade crossing."

A California motorist must come to a complete stop for a minimum of 3 seconds before continuing past a limit line.

CVC section 587: "Stop or stopping" when prohibited shall mean any cessation of movement of a vehicle, whether occupied or not, except when necessary to avoid conflict with other traffic or in compliance with the direction of a police officer or official traffic control device or signal.

59. The point to note is that the officer is actually making a measurement of the vehicle's displacement as a function of time as opposed to the angular velocity. Consider the front of the vehicle as the point of reference. The author defines time zero to be the moment when the vehicles are at the stop sign. Therefore, if we run time backwards we can obtain the position of the two vehicles at the two times, tp=-1.31s and tf=-0.45s. By definition, xp and xf for C1 are 8.61 and 1.00 meters from the stop sign respectively. xp and xf for C2 are 10.48 and 3.6 meters from the stop sign respectively where a velocity of 8 m/s was used. This tells us that C1 is always ahead of C2. Therefore, the officer would have a visual on C1 until the exact moment both vehicles reach the stop sign.

60. I think the mistake is that he left off the constant of integration?

61. ok, assuming that he is driving the Yaris Oxymoronic edition: tuned like a Ferrari in terms of acceleration, braking, tire friction, and suspension effectiveness; what about the weight shift being apparent in the suspension ie rear springs compressed under acceleration, front springs compressing under heavy braking? this would be apparent for the entire acceleration as a cue to changes in speed, unaffected by the cited theory

62. I actually had a similar incident. I got a citation for driving 75mph in a 55mph. I noted to the judge that the laser the cop was using was designed to work on a linear motion and I was driving a very crooked road, so it was impossible for the officer to measure my speed. In addition, the officer wasn't right ahead of me but was at an angle from a highway, which means the speed would have looked differently to him, depending on when he tried to measure my speed. Unfortunately, the judge wasn't impressed with my explanation. He reduced the ticket from 75mph to 66mph and reduced the fine by \$100, but I was still found guilty.

63. Dear Anonymous 11:01 PM: The error you are describing is called the cosine error, and IS ALWAYS IN YOUR FAVOR. Therefore, if anything, you would have been driving FASTER than you were clocked at. #FAIL

As is frequently the case in such matters, the solution is left as an exercise to the reader.

64. This is just another nail in the coffin of law that fails to account for relativity. What is the chain of custody for a radar reading from a particular frame of reference, and who vouches for the relative velocity of that frame?

65. 11:32 - no, that looks like a #WIN.

At least, arguing math in the court looks to me like a bit of leveling.

66. He is experiencing negative acceleration when approaching the stop sign. Not to mention that unless he is in a high performance car, he will not be able to match the magnitude his acceleration approaching the sign as leaving.

67. Looking at this and reading between the lines the issue and the reason he got let off has nothing to do with the main thrust of his physics analysis.

1/ He was charged only with not stopping at a stop sign.

2/ The officer did not contradict his statement that at the time he allegedly ran the stop sign the officers view was obstructed.

Therefore the officer cited someone for an offence he could not have observed directly, Case dismissed.

If the officer had also added a charge of careless driving for pulling through a stop sign wile not being able to see approaching traffic, as would seem he should have done from the evidence presented by the defendant.

Then his own evidence of the officers obstructed view would have convicted him on this second count, while exonerating him on the first.

I suspect that if the obstructing vehicle existed as recorded in evidence, then the officer was really trying to cite that other vehicle and the defendant was just in the way of his pursuit and so was just a convenient patsy.

If of course the other vehicle was not even there or did not obstruct then perhaps he got off due to a lapse of memory by the officer, combined with a lack of in-car video recording.

68. The pretense of an observer ( the cop) to determine visually whether the defendant car effectively stopped at the sign is not scientifically credible. The 'stop' rule is being complied to, as long as the second derivative of the car motion against time is annulled even if for an infinitesimally small duration. No human eye can capture this kind of timeline velocity, hence no cop can prove visually, beyond any doubt, that the car defendant did not comply.

For a cop to state beyond any doubt that the car did not annull the second derivative of it's motion against time, he would have to produce a timeline capturing sensor device whose rising time velocity is equal or greater than that of the time motion second derivative theoretical epsilon duration. This is equally impossible to establish given that the sensor velocity can always be measured, while the infinitesimally small second derivative duration can always be assumed to be smaller than anything that can be measured.

Hence while the defendant may or may not have stopped at the sign, a cop is never capable of stating beyond any doubt that the car did not comply with the stop rule, and therefore can be successfully challenged in court.

69. The comment below about a stop sign with a white border being "optional" is false, and a deadly misconception. All stop signs are mandatory.

That said, I want a car with 10ms^2 acceleration. That's Bugatti Veyron territory.

70. 3 seconds of complete stop?? Please post the exact section of the California Vehicle code where it says "3 seconds". You can't because it doesn't, not anywhere in the CVC. There is no such law. Yes, you must come to a complete stop, but that means that the wheels stop rotating and if they stop for a split second, that is good enough, according to the law. Prove me wrong. If you can't then you are spreading misinformation.

71. And dont forget that the maximum acceleration for a vehicle using friction traction is g. So for 10ms-2 he must have had rockets to help, of course.

72. I remember a case where the defendent threw an apple up in the air and asked the judge if he had seen it stop during the mid air travel. He then argued that because it had changed direction at the apex of it's travel, it must have stopped momentarily.

73. Stupidest discussion ever.

Shut the fück up, he won, deal with it.

74. I'm no physicist, and I'm not about to investigate whether or not a Yaris can accelerate at any given speed, because frankly I don't care. But--and I really hate to say this because the traffic ticket system is corrupt beyond measure and I think it should be destroyed--as an attorney, I think the flaw is that if he submitted documents purportedly based on physics and math swearing to things that, in real life, are impossible and did not take place; the flaw is that he submitted materially misleading documents to a court. In most jurisdictions the penalty for that is far greater than the penalty for a traffic ticket.

75. Smart move by the guy to switch to metric units, I wouldn't be surprised if because of that the judge didn't realize the severity of the acceleration. Not to mention that if the deceleration was instantaneous the jerk of the car probably would have broken a rib or two and that if it was quadratically shaped then the distance covered during the acceleration would have been like 50m (Assuming that he was going 22mph to begin with).

I don't feel like doing the math but the coefficient of friction between the brake pad and the tire and between the tire and the road must have both been really high for a 10m/s^2 acceleration to be possible and I highly doubt that it was close to high enough. Nor do I think that the engine of his prius could have generated nearly enough horsepower to enable such a steep acceleration.

-Engineering Student

76. The evidence that the defendant offered seems inadmissible - I am surprised it was allowed. Evidence must be in a form that may be understood by the uninitiated. Although high math is wonderful, you will find little in the court setting.

The argument that probably introduced sufficient doubt was the element of obstruction from another vehicle. The remaining verbiage seems excessive.

Arguing all the fine points are interesting, but nowhere in the paper are the practical safety considerations noted. It is not enough to have a brain. As other commentators point out, common sense and in this case an abundance of concern for safe operation of a vehicle, seem to be absent.

77. Perhaps after reading the technical details about velocity in linear or angular way a few times more, it would start making sense to simple minded people like me.

78. It's a pity that road safety has to take a backseat in this discussion.

79. Using the basic formula x=0.5at^2+vt+x0 it is easy to see that an accelaration of 10m.s^(-2)is out of reach for a Toyata Yaris! A distance of 100 m would be covered in 2.6 s which no legal vehicle can (as of today) do not even a McLaren F1! :)
Furthermore the same problem occurs for the decelleration of the car from 10m.s(^-2) to 0!
Lucklily for him, the judge has no knolegde of physics what so ever! :)

80. microstopping does not achieve the goal of safety. if you cant be bothered to pause a few seconds at a stop sign, then you probably shouldnt be driving. 30,000 people a year die on US roads and a lot of them can be prevented if people just slow down and stop being in a hurry.

81. While his total proof is flawed, it should be noted that even given that the police officer's view was possibly obstructed more more than 1/2 second, during which time the professor may have stopped and for which the officer cannot have known. That raises reasonable doubt, and hence without an actual unobstructed view witness or physical evidence the judge really had no choice but to throw it out. this probably had more to do with victory than his math.

82. I see what you did there, Anonymous 8:13 AM.

83. Maybe he had a custom top fuel Yaris. Top fuel dragsters accelerate at greater than 15m/s^2 (the fastest go up to 40m/s^2).

84. So, putting aside all the jargon and charts, his claim is that he slammed on the break, then the instant his car came to a stop he slammed on the accelerator. All of which the cop didn't notice because another car obstructed his view for that brief moment where the theoretical stop could have taken place.

Even if true that would mean he didn't take any time at all to look and see if cars were coming from the right or left, which is every bit as dangerous as not stopping at all.

85. Wow sounds like a really smart dude to me. Amazing

www.Get-That-Anon.tk

86. Sorry I did not read all the comments but there seems to be a bit of confusion between velocity and distance traveled over time.

If we assume that the car did stop and the angular velocity curve for the stop very closely matched the angular velocity curve without a stop after you remove the unobserved portion of the curve, the area under the curve is very different. That area under the curve corresponds to the distance the car has traveled.

After the obscuring car has passed, the officer would have observed the car as traveling at the expected speed but the car would have been in a different position that would obviously show that the car was not traveling at the same speed during the obscured period.

Very nice job confusing the officer, prosecutor, and judge and getting away with a flawed argument.

87. Without reading any of the other answers here, it seems pretty clear that the flaw in this argument is that his acceleration after the stop sigh could not have been the same as his deceleration before the stop sign. So if the office saw him at approximately the same speed after his "stop", he did not actually stop.

88. wow. what a poor explanation.
negative accel=positive. F1 car accel,etc.

Hope this guy doesn't have Tenure...

89. 10m/s^2, that's more than 1 g. If this dude could have done this with his car's headlight facing the heavens, he could have reached escape velocity in 983 minutes (No air drag) and left earth...

90. In order for the theory to work, the vehicle would still have to be in motion, therefore never stopped at the stop sign.

91. This seems to be about Humans ability to perceive motion or the lack of motion in a short period of time the flaw than is - that the other human perceived a stoppage of motion when in fact there was not, why? because he wanted to stop so he must have stopped,he had a cold and was feeling lousy so his head said ok you have stopped now go on.

92. The angle of the dangle is proportional to the heat of the meat; but the mass of the ass remains constant if relativistic effects are ignored.

93. I am a physics student in an AP physics class, and I was wondering if you would be willing to take the AP Test for me next month hahah thanks

94. The flaw?
The paper is dated April 1st...

95. It's also worthwhile to note that Eq. (18) is wrong. There should be no muliplier of 4. Although this mistake does not affect the value of t' at (20), it is worth noting.

And regardless of whether this is an April Fools prank or not, I'm happy that this paper was published because it has evidently inspired many to think critically and expose the flaws in his argument.

Kudos Professor Krioukov.

96. Don't understand why someone says this should be inadmissible, it's high school level physics, not "high math."

The acceleration numbers look unrealistic, but that's beside the point.

97. THERE IS ONE THING WRONG IN RHODE ISLAND THE LAW STATES THAT YOU MUST MAKE A 3 SECOUND STOP BEFORE YOU TAKE OFF WITCH IS ONE THOUSAND 1 ONE THOUSAND 2 ONE THOUSAND 3 THE TICKET WOULD HAVE PATD HERE

98. THERE IS ONE THING WRONG IN RHODE ISLAND THE LAW STATES THAT YOU MUST MAKE A 3 SECOUND STOP BEFORE YOU TAKE OFF WITCH IS ONE THOUSAND 1 ONE THOUSAND 2 ONE THOUSAND 3 THE TICKET WOULD HAVE PAID HERE

99. Does this mean that instead of the motorist having to go to Traffic School that the Officer has to go to Physics School?

100. The flaw is that the Judge did not ask the motorist what kind of transmission the car had. Was it automatic, or manual? I think the professor was driving (manual,)and if that was the case, no way he could have come to a full stop and accelerate without the police officer noticing the action.

101. I have successfully fought two collision insurance cases in small claims court using arguments based on physics and logic. My first comment is that the premise of this paper is nonsense, and it would obviously not succeed in court - it is therefore a fake. As for those who think an expert witness is not needed: during my first court case, I converted a miles-per-hour figure to feet per second, and the insurance company lawyer jumped up and objected to the judge that an expert witness was required to allow that. :-)

102. He could have just said there was a car blocking the traffic officers view of him stopping instead of all this bull.

103. This reminds me of a story a great Superior Court Judge told on himself. "When I tried my first case - speeding - in a small Arizona town, I went through all sorts of math to prove my client could not have reached the speed the patrolman said he reached in the distance involved. After the Not Guilty verdict was returned, I spoke to the jury foreman abour my brilliant defense, and how it impressed the jury. He replied - Aw no - we knew it was your first trial and we didn't want you to start off wilth a loss"

104. Glad to see that a few folks on here have gotten it.

Ignoring all losses, 106hp is not sufficient to accelerate a mass of 2295lbs at 10m/s/s. ... not even close!

105. The flaw was that he was actually guilty, the ticket should have been issued and let a judge decide the fate.

106. The law firm of Dewy, Cheatem & Howe would love this guy as an expert witness!

107. The judge let him off, because he took the time to write a paper. It is like going to jail or community service. Pay the fine or write a paper? You decide.

108. Very simply put (at least according to NH law) A stop is defined as a total cestation of movement for 3 or more seconds. His math/graphs show a stop of only 1 second. So 1st flaw is it was NOT a legal stop. 2nd flaw is that a true 3 second stop would considerably change the curve of the graph disproving the "illusion" said to be seen by the officer.

109. April 1st Joke!

Paper was published April 1st

110. The ticket was given and a judge did decide.
My response to Post:
Anonymous said...

The flaw was that he was actually guilty, the ticket should have been issued and let a judge decide the fate.

Tuesday, April 17, 2012 at 12:48 PM

111. It's been pointed out by others, but the flaw is the symmetric acceleration/deceleration rates. Accelerating at 10 m/s^2 from a complete stop is appropriate for race cars, not a compact Toyota Yaris. The car is physically incapable of accelerating this fast.

His proof hinges on accelerating really fast from a complete stop to produce the illusion. He never establishes a compelling reason to assume 10 m/s^2 for acceleration (to be fair, he does it for the deceleration rate), he just uses it.

112. I agree with this response! "Very simply put (at least according to NH law) A stop is defined as a total cestation of movement for 3 or more seconds. His math/graphs show a stop of only 1 second. So 1st flaw is it was NOT a legal stop. 2nd flaw is that a true 3 second stop would considerably change the curve of the graph disproving the "illusion" said to be seen by the officer".

113. This is what we used to refer to as a California pit stop. Although the wheels stop moving the body of the car continues to rock forward because of momentum and the fact that it is supported by suspension which is not rigid. Then as the gas is depressed the wheels catch up with the forward motion of the body so the entire car never stops completely at rest. Been their and done that and paid the fine.

114. I think most could find the answer at http://www.tampabayrescreening.com/

115. To the people that say a stop is defined as a cessation of movement for 3 or more seconds, that's not true as I was instructed by my driver's education teacher. While my mom used to tell me it was 3 seconds, my driver's ed teacher told me it just has to come to a complete stop. He even said "heck no, if you wait that long at a stop sign, people will take your turn and you'll never go.". That being said, I am from California! ;)

116. The one flaw that comes to mind is the fact that he sneezed while braking. it is merely impossible to sneeze with your eyes open which means that for a short yet critical time during the maneuver the driver was unable to see if the intersection was effectively still clear before proceeding forward (reason for the 3 second rules) and therefore crossed the intersection without verifying that it was clear of incoming fraffic

117. Now here is an application of math and science that shows how sweet it is.

118. In looking at the graph provided, the acceleration of the car would have to be as fast (the same) as the excelleration which was a result of slamming on the breaks.
I doubt that would be possible with this car.

119. Here is another reason to give to high school students when they want to know why I need to know this math and when will I ever need it!!

120. а на русском сможете доказательства привести..?

121. Is this not the same as factoring the dwell time of a reciprocating piston when taking into account different rod-piston-crankshaft angles for the same amount of stroke? i.e. 6" connecting rods vs. 5.7" connecting rods with the relocation of the wristpin centerline, while retaining the same crankshaft journal offset.

122. I can appreciate the dilemma of matching the rate of acceleration to the rate of deceleration. To an un-savvy traffic court judge this may seem plausible. This is a Yaris, not a 427 AC Cobra.

123. the flaw is clear: he assumes his car is capable of accelerating at the same acceleration it brakes... and, if he were driving a Ferrari, he wouldn't care about a \$400 ticket :)

124. Look at this we have a real life Dr.Shelton Cooper from the Big Bang Theory hence an idea for another episode

125. Failure to cite or reference an objective recording (possibly a recording from a dash-cam within the Officers vehicle) of the event and solely proceed on with the writer's subjective memory of the incident, fitting the math to the memory.

126. Stopping is only part of the law. Yeilding the right of way is also a requirement. A 10 m/s^2 stop that resulted from slamming on brakes because the defendant sneezed would hardly allow him an opportunity to proceed through the sign safely. Physics has created a probability but not a plausible probability. In addition, his acceleration after stopping would not equal his rate of decelleration from slamming on the brakes, so the graph is misleading.

127. all these folks claiming that a complete stop requires a 3 second pause at the stop sign are full of it.

doing the research (5 seconds of googling):

from the california driver's manual (the only legal reference that applies directly to this conversation):
"An eight-sided red STOP sign means you must make a full "STOP" whenever you see this sign. Stop at the white limit line (a wide white line painted on the street) or before entering the crosswalk. If a limit line or crosswalk is not painted on the street, stop before entering the intersection. Check traffic in all directions before proceeding."

at least one post specifically mentioned New Hampshire traffic laws, available here:
http://www.nh.gov/safety/divisions/dmv/documents/nhdm.pdf

there is NO rule in the driver's manual regarding a 3 second pause, or a pause of any duration, but only that the wheels must come to a complete stop (and that you yield when needed).

in other words, old wive's tales and rumors are being passed around as facts. anyone surprised?

128. In California, "stopping within six feet of a stop sign with no white limit line is substantial compliance with the law." From a real Calif. court (appeals) case, filed so historically far away in my note-taking of years ago that I will not take the time to find it. Use the Cal.Jur.2nd and related "digests" under "Automobiles > Stopping, Standing, Parking" or similar. I don't remember any required full-stop "time limit" in my lengthy research. The real purpose is merely to be alert and avoid collisions.

Most "rules of the road" traffic laws have been literally written in blood. As with seat belts, these laws protect us from the foolishness of others, protects others from us, and sometimes, protects us from ourselves.

Jury Trial for stop sign tickets? Not any more!

Now, "Title & Drivers License & Fee-Registration," there we find a wide and deep field for objections.

And for those who have Been There, Did That, Can't Remember: "I squandered the flower of my middle age in the law libraries." And others? Hmmm?

As for the \$400 ticket and the Ferrari, the rich got rich by Not Spending their money.

129. Al, an ex-physics professorApril 20, 2012 at 2:20 PM

People are confusing power (HP) with acceleration. Power = F*v = mass*acceleration*velocity

Note that power is a function of velocity, so, as velocity approaches zero, the power required to accelerate at any given rate approaches zero.

The max power required to accelerate at 10 m/s^2 to 10 m/s (the constant speed shown in the article) occurs right at 10 m/s. For a 1000 kg Yaris (the car described), this requires 10^5 Watts or 137 HP to achieve.

The standard Yaris is rated at 106 HP, so is a little under powered to hold 10 m/s^2 all the way up to 22 mph. However, even if the acceleration slowed between, e.g., 10 and 22 mph, that difference would not have appreciably changed the officer's perception.

The main performance requirements to achieve 10 m/s^2 (1 g) acceleration between 0 and 10 mph are tire grip and transmission gearing, not engine HP.

What you pay for in a Ferrari is rapid acceleration between, e.g., 60 and 100 mph and top speed, both of which require much more horsepower. :-)

130. There are some problems with this analysis; the obvious one that has been mentioned is the assumption that the deceleration of the vehicle equals the acceleration. The problems that I have, using the specifics of this case are:

1. The acceleration is given as acceleration=22.36 mph/s
The best acceleration this vehicle could accomplish = 9.41 mph/s

2. The schematic of the geometry of the considered case states that the officer was 32.81 feet from the intersection. This would mean the officer was approximately 65 feet from the defendants’ car. R0 should equal the distance from the officer to the defendants’ car. The distance from the officer to the intersection is irrelevant.
The distance R0 given = 32.81 feet
The actual distance R0 based on actual site geometry = 65 feet

3. Logically, for this given case to have occurred, the vehicle that blocked the officers view would have had to pass through the stop sign in order to obstruct the officers’ view at the moment the defendant R0 defendant stopped. The obscuring car could not have also stopped. Why wouldn’t the police officer chase and ticket the obscuring car for not stopping, as that would have been in plain view and occurred first?

4. As an aside, the penalty and fees of running a stop sign are \$235.00, not \$400.00. This isn’t important to the analysis, just interesting.

1. Curious... Where does 65 feet come from? Also, how is distance to the intersection irrelevant? Even if R0 is the distance to the defendants' car, the moment of interest occurs when the car is at the intersection. Oh...lane widths? Is that where the 65 is coming from?

131. As an addendum to my post directly above I have added the following graph that depicts the angular speed of the car observed from the Officer's perspective with respect to time.

Fig 1- Angular speed of car observed with real life variables

My conclusion is that in a real life scenario using the above mentioned numbers, this car decelerating/accelerating from/to 10m/s would need to be obscured for at least six seconds to mimic a car traveling at constant 10m/s velocity

132. As an addendum to my post directly above I have added the following graph that

depicts the angular speed of the car observed from the Officer's perspective

with respect to time.

Fig 1- Angular speed of car observed with real life variables

My conclusion is that in a real life scenario using the above mentioned numbers,

this car decelerating/accelerating from/to 10m/s would need to be obscured for

at least seven seconds to mimic a car traveling at constant 10m/s velocity

133. Who cares?
Laws are implemented in order to keep the paeans in their place, not to punish the educated elite.

A physicist is not an ignorant paean and should not be bound by the laws which were made to control the ignorant paean masses...We need this in America, or else we would have Presidents labelled as war criminals, Pentagon child-porn-downloading pedophiles filling our prisons, and Rush Limbaughs' convicted of drug offenses. None of which have the slightest chances of ever seeing a court.

As for commenters from other states trying to project their states laws onto Californian jurisdiction: Get a clue! Just because you live in a fascist state doesn't mean that anyone else in the world cares about your states peculiar rules; Running a stop sign may be a capital offense in some third world country, but this event occurred in California, not New Hampshire. What you accept in your state is not what we accept in ours!

In California, the police drive 85 in 25 mph zones, while talking on their cell phones (illegal for the average citizen), completely blowing through stop signs and stop-lights (they just flash their lights and siren). One officer was driving drunk, fell asleep at the wheel, drove across the freeway and crashed into a tree killing himself, and now his wife gets paid \$90K a year from the taxpayers because he "died in the line of duty".
Try that as a paean (read: normal citizen).

134. Could it be as simpleas the fact we assumed he was sneezing and assumed the sneezing caused him to press hard on the brake pedal causing an abrupt stop, when infact he may not have sneezed and actually did not stop as described. Furthermore, this is all based on assumption of facts rather than the facts themselves. It boils down to the principal of if you cant dazzle them with brilliance baffle them with bullshit.

135. What is considered the legal stop position or location of a car on approach to the stop sign and did he stop in that location.

136. I thought it might be April fools day joke, but it's been shown not to be

137. For all of you experts the car has to "rock back" at the stop sign to make it obvious to the cop and others that you have stopped. You do not have to launch your car from the stop sign like a Formula 1 car either. Be reasonable. If you sneezed please wipe your nose and be careful so you do not hit the car in front of you. That may require slowing down and even stopping at the STOP sign! For the physics professor please make your car "rock back" (that means zero speed and some negative speed too) so you do not get caught at a weird angle next time.

138. Angular velocity is not the whole story; you must also consider distance. If Krioukov's car accelerated at 10 m/s for the entire 10 sec before and after stopping (Figs 3 and 5), then 10 seconds before and after stopping his car would have been going 100 m/s (224 mph) and would have been 500 m (1640 ft) from where he stopped. If his car had been traveling at a constant 10 m/s speed (22.4 mph) without stopping (Fig 2), then 10 seconds before and after stopping his his car would have been 100 m (328 ft) away from where he should have stopped. A car looks a lot smaller 1640 ft (0.31 miles) away than 328 ft away. The police office could easily have noticed the difference. The numbers would become even more absurd if Krioukov assumed accelerations greater than 10 m/s to shift his double peaked Fig 3 curves closer to the time at which he supposedly stopped in an effort to better mimic the spread in the Fig 2 curve.

139. Just a correction to the price of the California ticket. The base fine for 21453 is \$404, not \$235; however, with fees and assessments, the total comes to \$480.

140. Doesn't this presentation presume and require that car #2 (C2) ran the stop sign while blocking the view of car #1 (C1) which was allegedly stopping? Wouldn't the officer therefore have noticed the C2 vehicle as being the primary offender, esp. since it was closest to the officer and in plain view? Furthermore, wouldn't having the two vehicles side by side offer a comparison opportunity, i.e., if car # 2 blows through the stop sign, then car # 1 would appear to stop as it would be lagging behind car #2 (if indeed car#1 stopped). Similarly, if car #2 was directly witnessed to have stopped, then wouldn't that provide a comparitive to determine similar/different behavior of car #1 behind it? I can see this working if car #2 were turning right from the right lane of C1 and C2's shared street, and therefore blocked the view to C1 while failing to give a relative behavior to compare; especially if car #2 had to pause for an oncoming vehicle before completing his turn. But, I don't see it working of C#2 continued to parallel c#1, and thus offering a relative behavior to go compare.

141. Date of publication in the UCSD campus newspaper... April 1.... Think about it !!!!!

142. OK folks - take this as example of how the internet works. HP and many other sites have posted and reposted this story. Check out the link to the original paper - and pay attention to the publication date before you try to wrap your head around the physics. April 1st. Does that date mean anything to you ???? Yes - this was a gag... now picked up and repeated within the echo chamber of the internet. Yes, I do hold several physics degrees.. But really people - you should not need to check the math on this item to understand what's really happening!

143. I hereby nominate Dmitri Krioukov for the 2012 Ignobel prize in physics

144. I believe that one flaw is as follows: police use Doppler radar to measure the speed of their targets. The Doppler shift is proportional to the dot product of the direction of propagation of the radar wave and the direction of travel. Therefore, if the police was perpendicular to the direction of travel, as is the case in the diagrams, then the Doppler shift will be zero and the police will not measure anything.

145. Well, if correct expression is used instead of (8), where initial velocity is not missed, the resulting observed angular rate would never be misinterpreted ...

146. I think I've been a passenger in a car with this exact situation 40 years ago. There is no question that a friend of mine made a quick full stop at stop sign, but was issued a citation for running the stop sign. There was an obstruction, and the officer's position was almost exactly as described.

147. That's such an amazing way to get out of traffic tickets! I love this guy!

148. As it is physically impossible to keep one's eyes open while sneezing, I suggest that he continued his deceleration right on through the stop sign... only to come to a stop after having passed, ever so slowly, through it.
His perception of events may be flawed, just as he suggests, the citation issuing officer's were.

149. A Bocelli, true eventDecember 24, 2012 at 10:24 AM

Hey I beat a ticket like this also. I had a red light ticket.
I didnt run the light but the officer claimed I did.
I proved 2 things , 1 he could not see the light controlling my direction of travel to testify what color the light was.
2. he information was incorrect about the lane of travel and position of my vehicle. I big work truck.
Dont ever think a ticket means your guilty unless you know your guilty.

150. There is a big hole in this argument. If the car that blocked the Officer's view zoomed through the intercection, without stopping, the Officer will still be able to see Dmitri waiting at the stop sign. On the other hand, if the other driver stopped, the Officer would have noticed Dmitri stopped. A stop at a STOP sign will take a minimum of 1 second, looking left and right before proceeding. A car traveling at 20 mph will travel past the STOP sign in a fraction of a second, still leaving enough time for the Officer to see Dmitri stopping at the STOP sign. The Judge was either confussed or impressed by the law breaker.

151. This is fantastic!!

152. Not all parts of an automobile move at the same speed the top of the wheel moves at twice the speed. Radar detectors are exaggerating the speed of motor cycles which have exposed spokes. Traffic cameras detect cross sectional area motor cycles have to get closer to trip the stoplight this leads to more run red lights because the yellow light has a shorter cycle if no traffic is detected. Sensors in the roads detect metal motorcycles have to get closer to trip the sensor this also leads to more run red lights. Bicycles are generally unable to be detected by all three means this leads cyclist getting speeding tickets because the radar detected an automobile behind it or running red light tickets.

153. To the Anonymous poster who repeatedly used the word
"paean" Please, look it up. I believe the word you're really reaching for is "peon". Your average citizen is not a "A song of praise or triumph." ;)

154. i think he never stop, anyway good trick

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156. Your "quick stop" is called a "rolling stop" and it's illegal

157. Problem is there is no stopping time at the stop sign. From what I remember you are supposed to at least remain at the stop sign for about, 3 seconds? before you can accelerate again. There could also be another issue depending on how fast the other car blocked the view.

158. This all would have been much easier if he just had a radar detector. They actually use physics, no papers or equations are required. He could have read some radar detector reviews to get information, rather that doing this.

159. No complicated physics involved. But a Yaris would have a hard time accelerating at the same rate that it could decelerate under maximum braking force. FWD, little economy cars are not known for acceleration. Also, from a practical standpoint, the stop indicated by the graph is not enough time for the human brain to observe the intersection and determine that it is safe to proceed. This is just one more flaw to add to the bag, not THE flaw, just one more.

160. Whoo.. That was something. Though we are not physicist, we play tricks too. People who are good at something uses that knowledge to play trick on others. Here, he was successful in applying the trick through physics, though not legal. Tricks if failed could lead you into trouble. Drive safe.