Proof of Innocence Reproducing the Event BY JOHN

Proof of Innocence Reproducing the Event BY JOHN S. OCHAB, PH. D. PROFESSOR OF PHYSICS WITH KENT RITCHIE UNIVERSITY PHYSICS STUDENT J. SARGEANT REYNOLDS COMMUNITY COLLEGE RICHMOND, VA

HEADLINE NEWS Physicist Beats Traffic Ticket With Math - ABC News - Go. com Scientist uses physics to beat $400 ticket - CBS News Physicist Writes Mathematical Study to Avoid Traffic Ticket. . . Buzz Blog: Physicist Uses Math to Beat Traffic Ticket Dmitri Krioukov, Physicist, Writes Four Page Paper To Avoid. . . 1

The Event – Author’s Car Stops at Sign and Proceeds Police uses Personal Vision instead of Radar

Geometry of the Author’s Car approaching the Stop sign, without obstructions, as eye-witnessed by policeman at point, O. v X 10 m 32. 8 ft R 0 = 10 m O O

Author’s 1 calculations of the Angular Velocity, , of his Car as a function of Time, t, for Constant Speed through Stop sign

Angular Speed, , vs. Time, t, graphs of Author’s car based on the author’s calculations (without obstructions) Car passes through Stop sign at Constant Speed (10 m/s 23. 36 mph)

Author’s calculations of the Angular Speed, , as a function of Time, t, of his Car “stopping” & “going” through Stop sign.

Graphs 3 of Distance vs. Time and Speed vs. Time of a car “stopping” and “going” at a traffic light Model was based on extensive real-life driving data representing general driving conditions, involving a wide range of speed change cycles on different road types. Distance Speed Deceleration is not a constant. Acceleration is not a constant.

Angular Speed, , vs. Time, t, graphs of Author’s car based on his calculations (without obstructions) Car Decelerates (to full stop) and Accelerates away from the Stop sign at various, but constant, accelerations, a 0.

Angular Speed, , vs. Time, t, graphs of Author’s car based on the author’s calculations (without obstructions) Car passes through Stop sign at Constant Speed (10 m/s 23. 36 mph) Car Decelerates (to full stop) and Accelerates away from the Stop sign at various rates.

Desmos Graphing Calculator https: //www. desmos. com/calculator Angular Speed when traveling at Constant Speed, v 0, through Stop sign:

Our Setup – Top View

Our Setup – Side View

Measuring the Angular Speed, , and Linear Speed, v, of the hand-pushed Black box guided by the edge of a Pasco track. v My hand Top view Laptop x Pasco Linear Motion Sensor X = 20 cm R 0 r 0 Ointo = 22. 7 cm Pasco Rotary Sensor Pasco Scientific 850 Universal Interface

Demonstration of Data Acquisition Angular Speed when traveling at Constant Speed, v, through Stop sign. Angular Speed when Decelerating, to a full stop at Stop sign and Accelerating, away from Stop sign.

Comparison of Angular Speed vs. Time graphs for Author’s car and for Black box, both traveling at Constant Speed through Stop sign Author’s Car Black box Sample rate: 40 Hz

Angular Speed versus Time graphs as before, including a Linear Speed versus Time graph of the Black box Author’s Car Black box Sample rate: 40 Hz Angular Velocity, Linear Speed, v

Comparison of Angular Speed vs. Time graphs for Author’s car and Black box moving at a faster Constant Speed through Stop sign Author’s Car Black box Sample rate: 40 Hz Angular velocity, Linear Speed, v

Comparison of Angular Speed vs. Time graphs for Author’s car and Black box both “stopping” and “starting” at Stop sign. Author’s Car Black box Sample rate: 40 Hz Peak-to-peak time duration = 0. 575 s

Comparison of Angular Speed vs. Time graphs for Author’s car and lab box both “stopping” and “starting” at Stop sign. Author’s Car Black box Sample rate: 40 Hz Peak-to-peak time duration = 0. 425 s

Angular Speed vs. Time and Linear Speed vs. Time graphs of Black box “stopping” and “starting” faster at Stop sign. Sample rate: 40 Hz Peak-to-peak time duration = 0. 275 s Peak-to-peak time duration = 0. 225 s

Angular and Linear Velocities vs. time graphs of Black box “stopping” and “starting” faster at Stop sign. Sample rate: 40 Hz Peak-to-peak time duration = 0. 200 s Peak-to-peak time duration = 0. 175 s (My hand cannot push any faster!)

Comparison of Angular Speed vs. Time graphs for Author’s car and Black box both “stopping” and “starting” at Stop sign. Author’s Results Our Results t =0. 175 s t =0. 275 s

Definitions of Full and Partial Obstructions by Another Car Lane 1 Lane 2 Suburu? Full Obstruction, Subtract car lengths O Partial Obstruction, Add car lengths O

Author’s Diagram Showing Full Obstruction by Another Car when both cars are near the Stop sign. Toyota Yaris Lane 1 Suburu? Lane 2 Author’s length, l 1 = 3. 81 m l 1/ l 2 = 0. 8 R 0 = 10 m Other car length, l 2 = 4. 80 m xpartial = l 1 + l 2 = 8. 61 m xfull = l 2 - l 1 = 0. 990 m O = 1. 31 s = 0. 445 s

Author’s calculations for determining the time at which his Car’s Angular Velocity goes over it’s Maximum Value (without obstructions). tfull = 0. 445 s < t’ < tpartial = 1. 31 s

Author’s Calculations of Time Duration, tb, due to obstruction by buildings, adjacent to lane, L 2, on opposite sides of the intersection Lane 1 Lane 2 L 10 m R 0 = 10 m L = Distance between buildings 1. 07 s t’ O

Angular Velocity vs. Time Graphs of Author’s car with obstructions from another car and from buildings on opposite sides of the intersection. Dotted lines show time durations for partial obstruction, tp, and for full obstruction tf. t’ is the time duration at amax. Since tb t’, we can cut obstruction from buildings. Greater proof!

Determining the time at which the Black box goes over it’s Maximum Value (without obstructions). Sample rate: 40 Hz Peak-to-peak time duration = 0. 175 s =0 a = -0. 540 m/s 2

Diagram Showing Partial Obstruction of Black box by a fictitious box when both boxes are near the Stop sign L 1 = Lane 1 80% longer Black box length, l 1 = 0. 140 m L 2 = Lane 2 l 1/ l 2 = 0. 8 R 0 = 22. 7 cm Obstruction length, l 1 = 0. 175 m 80% longer xpartial = l 1 + l 2 = 0. 315 m xfull = l 2 - l 1 = 0. 035 m tpartial = 1. 08 s O tfull = 0. 360 s tfull < t’ < tpartial

Comparison of vs. graphs for Author’s car and Black box both “stopping” and “starting” at Stop sign showing Full and Partial Obstruction Time Intervals t partial Peak to peak t = 0. 175 s t full t’ -1. 2 -1. 0 -0. 8 -0. 6 0. 8 1. 0 1. 2

Conclusions Ø Our experimental results seem to substantiate the author’s claim that the policeman’s visual measurements were delusional. Ø Peaks in the Angular Speed graphs for Stop and Go approach peak in the Angular Speed graphs for Non-stop, as the rate of deceleration/acceleration of the car increases. ØIn reality, a car could not go that fast to produce that result. ØObstructions due to a nearby car adds to the delusion. Ø Buildings’ contributions can be ignored. Ø A better experimental method is needed for stopping and starting the black box (or other object) faster, and more closely associated with a real car. Ø Suggestions for a better method? Ø Good lesson plan for students?

How I Fought Traffic Tickets using Physics

“I could not determine if the light was red. It was beyond the 30 limit of my field of view. ”

“I was not speeding due to the Cosine Effect”. 30 http: //copradar. com/preview/chapt 2/ch 2 d 1. html Terminix

THANK YOU! References: [1] [ http: //arxiv. org/pdf/1204. 0162 v 2. pdf [2] Acceleration and deceleration models, Rahmi Akçelik and Mark Besley, Akcelik & Associates Pty Ltd, 23 rd Conference of Australian Institutes of Transport Research (CAITR 2001), Monash University, Melbourne, Australia, 10 -12 December 2001 Revised: 11 July 2002 [3] Ibid.

Extra slides follow

Comparison of vs. graphs for Author’s car and lab box both traveling at “constant speed” through stop sign Author’s Car

Comparison of vs. graphs for Author’s car and lab box moving at a different “Constant Velocity” through stop sign Black box Author’s car Count rate: 20 Hz

Comparison of vs. graphs for Author’s car and lab box both traveling at “constant speed” through stop sign with faster count rate. Author’s Car Black box Count rate: 40 Hz

Angular velocity, , versus time, t, of car “stopping” and “starting” at stop sign. Count rate: 20 Hz Author’s Car Experimental Graph Black box Peak-to-peak time duration = 0. 900 s

Car “stopping” and “starting” at stop sign. Count rate: 40 Hz Peak-to-peak time duration = 0. 550 s

Car “stopping” and “starting” at stop sign. Experimental Graph Count rate: 40 Hz Peak-to-peak time duration = 0. 450 s

Partial Blocking of Black box with Purple box that is assumed moving at Constant Velocity parallel to Black box. v My hand Top view Laptop x Pasco Linear Motion Sensor X = 20 cm R 0 r 0 Ointo = 22. 7 cm Pasco Rotary Sensor Pasco Scientific 850 Universal Interface

Comparison of vs. graphs for Author’s car and Black box both “stopping” and “starting” at Stop sign showing Full and Partial Obstruction Time Intervals t partial t’ t full Peak to peak t = 0. 175 s

Diagram Showing Partial Obstruction of Black box by a fictitious box when both boxes are near the Stop sign L 1 = Lane 1 80% longer Black box length, l 1 = 0. 140 m L 2 = Lane 2 l 1/ l 2 = 0. 8 R 0 = 22. 7 cm Obstruction length, l 1 = 0. 175 m 80% longer xpartial = l 1 + l 2 = 0. 315 m xfull = l 2 - l 1 = 0. 035 m tpartial = 0. 527 O tfull = 0. 176 tfull < t’ < tpartial