Speed = Distance / Time. HELP Basic grade school math.

  1. ClA

    ClA 7

    Speed = Distance / Time. HELP!! Basic grade school math.

    Hi, I am not super good in math so I really need some help with this math problem. I just got an unfair speeding ticket and I need to prove that the officer's speed calculation was incorrect.

    I am pretty sure this will be very simple for the rest of you.

    I was traveling 65 miles per hour for 3 miles, this took 2 mins and 46 seconds as calculated by this website.


    The officer was from a stop and he started chasing after me claiming that I was speeding (limit was 65mph). He used his own speed to determine what my speed was.

    Now, if he went from a complete stop, and drove 3 miles in 2 mins and 46 seconds, how fast was he travelling when he caught up to me??

    :cry: Please help. Maybe you can show the calculation as well so I can show the judge. Thank you very much.
    Last edited: May 7, 2007
  2. jcsd
  3. hage567

    hage567 1,538
    Homework Helper

    How much over the speed limit did the police officer say you were going?
  4. ClA

    ClA 7

    He put down 75mph. Which I believe was the speed he used to catch up to me since he came from a complete stop to catch up to my car. He used that speed to determine that that was the speed I was travelling at, which does not make sense.
  5. cepheid

    cepheid 5,189
    Staff Emeritus
    Science Advisor
    Gold Member

    Ok, first of all, he must have had good reason to suspect you were speeding before he took off after you, otherwise, why would he have started chasing you in the first place? Are you sure he didn't have photoradar or something? Also, how could you possibly know that he chased you for exactly 3 miles before he caught up with you? Despite being chased by a police car, did you suddenly have the presence of mind to reset your odometer at the precise moment that he started moving? I'm dubious. Also, if you saw a police cruiser chasing you, sirens blaring, why didn't you just slow down and/or pull over like any sane person rather than continuing to drive at a constant velocity, ostensibly for 3 miles, waiting for him to catch you? Especially if it took nearly three minutes, which is a long time!
  6. cepheid

    cepheid 5,189
    Staff Emeritus
    Science Advisor
    Gold Member

    For what it's worth (I'm bored right now), taking everything at face value (I'll use x for distance)

    I'll assume the cop accelerated uniformly from rest. The distance the cop travelled as a function of time, assuming he started at rest is:

    [tex] x(t) = \frac{1}{2} a t^2 [/tex]

    a is the acceleration

    t = 2 min 46 s = 2.7667 min = 0.046111 hr


    x(0.046111 hr) = 3 mi = 1/2 a(0.046111 hr)^2

    [tex] a = \frac{6 \ \textrm{mi}}{t^2} = \frac{6 \ \textrm{mi}}{(0.046111 \ \textrm{hr})^2} = 2821 \ \frac{\textrm{mi/h}}{\textrm{h}} [/tex]

    By definition, the speed, or magnitude of the velocity, v is given by:

    v = at

    = 2821 mi/h^2 * 0.046111 hr = 130 mi/h

    So, if any of what you have said is accurate (and I have huge doubts as I outlined in my previous post), then in the ideal case that he just kept going faster and faster, the cop was going way faster than 75 when he caught up to you. Of course, in real life, he would decelerate upon his approach, so we really have no easy way of knowing exactly how fast he was actually going, and I highly doubt that it matters, because I'm sure he exercised reasonable judgement in estimating your speed.

    P.S. I wouldn't present this calculation to a judge if I were you.
    Last edited: May 8, 2007
  7. ClA

    ClA 7

    This is off topic but if it interest you, i'll let you know.

    The officer claimed that he used radar when I drove pass him, which in fact he didn't (as he did not mark the "radar box" on the ticket). He said he followed me for 3 miles which was a lie. From a stop position, he gained speed and got up to my car for no more than 5 seconds, then pulled me over with his lights. He did not chase me for 3 miles. He pulled me over 3 miles from where he began from the stopped position.

    All the questions you asked above can be answered with this: I had a video in my car and I recorded the whole thing including the conversation we had when he pulled me over. The 3 miles etc etc everything is based on the officer's own words, which at times contradicted himself. All was caught on camera.
  8. ClA

    ClA 7

    Thanks for that.

    Yes, based on the results of your calculations, I don't think this will help my case much.

    But your calculation seem correct. The officer was coming from behind pretty fast when he came up to me. I would say 90 to 100mph. He got up behind me for 5 seconds and started flashing his lights. At first he said he got me with radar, then he said he didn't use radar......then again he said he did used radar.........and at the end.....he said he used the bumper pacing method. Which all contradicted itself.

    All this was caught on tape. I just wanted additional prove of his speed when he come up upon me as evident that using his speed was not a good way to determine mine. But I guess 130mph was a bit too much.
  9. rcgldr

    rcgldr 7,690
    Homework Helper

    Depends on his rate of acceleration. Assume he accelerates from 0 to 80mph in about 1000 feet, taking about 15 seconds, which is fairly slow. He's averaging 45mph for 15 seconds. During this time you travel 1430 feet, giving you a 430 foot lead. He gains 22 feet / second on you, so it takes 19.5 seconds to catch up. In this time, you've traveled another 1865 feet. It took him 34.5 seconds to catch up which is 3289 feet, about 0.62 mile.

    However you can forget the math. Cops sometimes make not so honest mistakes. I get the feeling that some will just hand out one bogus ticket every now and then, maybe when they are in a bad mood, since there's little chance they'll ever get caught. Worse yet, you could be driving the same type of car that the guy the cop's wife is cheating with.

    There's no system in place to allow the public to complain about bogus tickets, so that cops with an unusually high rate of complaints could be monitored.

    My very first ticket was for going in excess of 45mph in a 25mph zone, it was a cop on a motorcycle, and his max speed was 50mph (a fixed needle moved by the speedometer to the cop's max speed, this was the late 1960's). I was driving a moped, barely going 30mph, up a long upgrade, at the border between two cities where the speed transitioned from 25mph to 35mph. I was stopped 1 mile past the border where the speed limit was 35mph. There were cars in front of me pulling away.

    Other "bogus" tickets. Back in the old days of the 55mph speed limit. Cop is in #4 lane ahead of me doing about 45mph. It's night time. I'm driving a motorcycle in the #1 lane, and the only reference point he can see is my headlight. The cop sees my headlight in his mirror and estimates my distance at 300ft, uses a stopwatch to "clock" me, pulls me over and issues me a ticket for doing 60mph in a 55mph zone.

    Another one from the 55mph days. I'm doing about 58mph in #1 lane, again at night, constantly pulling over into #2 lane to allow faster traffic by. A cop gets onto the freeway, gets behind me, and I pull over to get out of the way, he turns on his lights, so I continue going right past #4 lane and stop on shoulder, before the next off ramp. I get another 60mph in 55mph zone. Total distance between on ramp and off ramp was less than 1/4 mile. Obviously there was no attempt to actually measure my speed.

    Most incredible ticket ever? A V-Twin Honda motorcycle RC-51 (130hp) clocked by aircraft at a claimed 205mph. It has a top speed around 165mph, under ideal conditions, and the reality is that 160mph would be unreachable. The aircraft was clocking two different motorcycles, and it's pretty clear that he either switched them or had an issue starting and stopping a stop watch. However the cop refused to admit he made a mistake. To reach 205mph, the motorcycle would require more than double the power at about 273hp. Then again, the ticket was $215.

    I live in California, and as long as you don't get a ticket more than once every 18 months, you can go to traffic school and not have the ticket show up on your record, although you still pay the fine. The few times I've been in traffic school, it became pretty clear that a small percentage of the people there were truly innocent.

    You stand little chance of winning a case in court if you claim to be a victim of a cops mistake (honest or not). Considering all the other bad stuff a small percentage of cops do, issuing bad tickets is very low on the list of priorities in the system.
    Last edited: May 8, 2007
  10. ClA

    ClA 7

    Thanks. I am in California too. You'd be surprised how many bogus tickets are handed out each day. I beat 3 of my last 4 tickets already. Cops have quotas to fill and that is actually true.

    My friend just got a ticket today for going downhill in neutral gear.


    He drove an 18 wheeler truck where he sat about 6 feet off the gound. How the hack can a cop know what gear he was in?? Its not like he can see it. My friend will fight it and he will win. Burden of proof is on the cop's side, there is no way he can prove he was going downhill in neutral.

    We both laughed at it.
    Last edited: May 8, 2007
  11. ClA

    ClA 7

    My gosh you for real?? 60 in a 55? Over by 5 miles per hour? I doubt an officer can reasonably prove the 5 miles difference........impossible.

    Yes, I figure the rate of acceleration should play a part in this calculation. Which is where I got stuck. I don't think this will matter in court anyways........but I know people that've beat tickets using equations to prove the cop's argument was incorrect.
    Last edited: May 8, 2007
  12. ClA

    ClA 7

    haha sorry I laughed at this. Oh my gosh that was complete bull crap. Seriously, if you fought it, that would be an easy win for you.

    I beat 3 out of 4 of my last tickets. You should really check this site out......fighting tickets by mail (California only). No need to show up in court.

  13. rcgldr

    rcgldr 7,690
    Homework Helper

    Nothing in that statue about depressing the clutch. How could they prove that your friend wasn't depressing the clutch as opposed to being in neutral?

    During the Carter and post Carter 55mph era, the feds were really pushing states to enforce 55mph by threatening to take way highway funding. Early on, what was accepted as proof of speeding was really bad. As time went on, eventually most of these methods got invalidated by lawyers and the courts.

    What was eliminated:

    Estimating speed by simple observation from a fixed point, some officers were claiming they could accurately estimate a cars speed simply by observing a car going by. When actually tested, it turned out that their estimates were affected by the size of the car, and were quite off with smaller vehicles like motorcycles (they overestimated the speed of small vehicles, underestimated the speed of large vehicles, like trucks, due to perpective which there is a thread in this forum that discusses this).

    Estimating speed of a car approaching a cop vehicle from behind (unless it was to simply state that the vehicle caught up), since it requires accurate estimate of distance behind, and most drivers "slowed" down and never really caught up, unless the cop also slowed down.

    In California, the usage of a hand held stop watch for any speed estimate, including aircraft. Aircraft patrolling is still allowed, but all they can do is radio for a ground based policeman to use a radar gun to verify the speed of the car.

    Tickets for going just 5 mph over the speed limit are extremely rare, and probably limited to a cases like going 30mph in a school zone with kids present. This only existed for the first 2 years of the 55mph speed limit change. Eventually just about every method other than radar was shown to not be accurate enough to gage this difference, and the tickets were getting thrown out of court. In my case, the judge changed my fine to $10, since I got the ticket in a city 40 miles from my house and couldn't take the time to fight it in court. In this particular city and time the judges weren't allowed to dimiss tickest on their own without a trial.

    Note that the 55mph speed limit wasn't truly nation wide. The federal government can't set speed limits directly, but what they did do was threaten to withold federal highway funding if states didn't change and enforce the 55mph speed limit. There were a few states that got little or no federal funding, so they never implemented a 55mph speed limit. If I remember correctly, Montana had no speed limit at all (just a basic speed law), until a few years ago. 100mph on a rural road with no traffic seemed to be the "real" limit, as tickets for 100mph were getting thrown out for not exceeding the basic speed law (speed it was safe to travel at). Arizona had and has the highest posted speed limits, 85mph, mostly for the interstate freeways. Motanta has a 100mph limit now, but it's not posted.

    But in your case the cop had almost 2 miles to "clock" you. In the cops mind, you probably slowed down once you saw him so he went by his initial estimate of your speed, long before he got close enough to truly pace your speed. Since it's not required for the cop to state how long (how many seconds) he actually paced you at a reasonable distance to verify your speed on the ticket, the difference between reality and what the cop states in court can vary quite a bit. Many police cars have dashboard cameras, and there are radar systems that work with moving vehicles. One way to eliminate the lies would be to include telemetry in the recorded video from the dashboard camera (the cops speed, and the victim's speed if possible), and require this as proof in court. Currently the only video requirement is for the red-light cameras. My wife got one of these, because it turns out that these systems estimate that a driver is going to run a red light and start video taping when this occurs, then camera shots are taken. In my wifes case, she was making a right turn on a red light and she stopped, but it turned out that the sensors were set a bit too far back of the limit line. Turns out that only about 1/3rd of the stop light tickets ever get passed the review stage, and in most cities all are reviewed before mailing a ticket out. This particular city is a bit lazy/greedy and only review tapes when a victim schedules a review, and the victim has to show up for the review, a bit of a hassle but otherwise a similar procedure. The reviewing officer can dimiss the ticket without requiring a judge.
    Last edited: May 9, 2007
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