I just got pulled over and received a ticket...the problem is, I don't think it's physically possible that I was going as fast as the officer claimed I was. I pulled out from a standing start on to the road he was sitting on, and he said that he clocked me at 40mph even when I reached him (25mph zone). The cop refused to accept that I couldn't have been going that fast. My intention is to prove in court that it's not physically possible...I really don't think it could have been more than 100 feet.

I did some digging through articles, etc. which indicate that the Z should be able to reach 40mph in 3.4 seconds. I've been playing around with the algebra on this, and keep coming up with slightly different answers. Could someone please verify the distance in feet necessary to accelarate to 40mph in 3.4 seconds?

Conversions:
1 mph= 1.467 feet/sec
1 ft/sec= 0.6818 mph
1 mile= 5280 feet
1 ft= 0.0001894 mile

As I said, I keep coming up with slightly different answers, so I'd appreciate it if someone could do a math check for me...thanks!

 

your problem is that you are dealing with acceleration rather than a constant velocity.

You need to figure out how many ft/sec/sec a Z accelerates at.

I know that at max accelration, the Z sees a G force of approx .7G's this slows after the 1st shift.

1 G is 32ft/sec/sec

So the Z accelerates at approx 22ft/sec/sec for the first couple seconds

If the Z hits 40 in 3.5sec, then I estimate is would hit 40mph in 250-300 ft.

Rather than work the problem backwards though why not just mark a line and then accel to 40mph. Have an assistant mark the spot at which you hit 40mph. Measure the distance.

 

You need to know a number of inputs:

- at what point(RPM) did you shift
- the exact distance

You can however do the fastest scenario:

Go and get a copy of car&driver, I believe it had published the curve which shows time vs. speed.

You have to base your distance on that graph since the speed is not linear between zero and 40 MPH. If, according to the speed shown on the curve, it is impossible for you to attain that speed in the distance (100'), you have to get the cop to submit/admit the distance.

Let me know how the calculation goes.

 

Ok...I kept running in circles trying to work with linear acceleration, which we're clearly not dealing with.

N74DV...if I do an indepedent test, it won't hold up in court...various data points from a respected magazine(s), with a pro driver, doing full blast acceleration runs is much more valid. If their times can't cut it in that distance, it will be hard for them to try say I could!

DumbGenius,
I actually have that magazine at home...but I'm not sure I understand your method.

Let me take a shot here...so I need to calculate the acceleration at the various points up to 40mph on the curve. Here are the actual time and speed numbers from a road and track article (vs. 911, M3, Z06). Three points are enough to make a curve, right?

0-20mph = 1.4 secs
0-40mph = 3.4 secs
0-60mph = 5.8 secs

Here are the numbers from Car and Driver:

0-30mph = 2.0 sec
0-40 = 3.1
0-50 = 4.1
0-60 = 5.4

But I'm still trying to figure out how to calculate the distance traveled at each of these points. Do I have to calculate the slope of the curve for these points? Thanks!

 

Unfortunately, even magazine & newspaper articles do not have sufficcient evidenciary foundation.... You may get lucky, but a good prosecutor and/or judge will object the second you try to introduce a magazine article as evidence.

Reason being is the article itself cannot be cross examined... Your best bet is to videotape an experiment yourself with one or two witnesses. This way you can introduce the tape as evidence because you yourself created it and you can be cross examined as to the methods and conditions in which the experiment was conducted. Your can subpoena your witnesses to testify as to the authenticity of the experiment as well.

If the judge allows you to introduce the tape as evidence he has to take it for what it is... not his "opinion" that you may have staged it in your favor.

I'm no lawyer, but I know the court system well and how court proceedings go.

do a search on "laying foundation" for your evidence and you'll see what I mean....

I'm going to court next month to fight a ticket... I fully expect to win!

 

first things first. measure the distance, youll need photos of the area, with a tape measure laid out.

next for equations, simple physics equations

you can use the number they got, all you need is that you started at 0 and ended at 58.68ft/sec, this occurs in a minimum of 3.4seconds.

Velocity/time=accel

this means you can use average acceleration 17.25/s/s

ok, now you need to know how far this is?

.5*A*T^2

.5*17.25*3.4^2

99.705feet.

sorry man, but it would seem that you are able to do it... go back and check the distance, see if that helps... but according to this, if you did full throttle youd hit 40 in exactly 100 feet.

 

Here is your official answer. 3.0 sec to get to 100ft, and 3.3 to reach 40mph. So if it is exacly 100ft you in the clear, but if it was 10ft over you might be in trouble.
here is the evidence I found. http://roadandtrack.com/reviews/road..._350z_data.pdf

 

Ares,
That's the calculation I was digging in my head for...thanks!

I think i might be F'd...it's going to be close, but I think they might have me. I'll measure the distance soon.

Thank you all for the advice and methodology...much appreciated. My court date is not for a month, so if this doesn't work, maybe I'll figure a new way to get out of this...grr...

 

The responses you have received from people far smarter than I would indicate that you have a very complicated equation to explain the judge. Even than, wowing him with math may not be the best defense. I have seen a post here regarding fighting a ticket. The defense is based upon attacking the cop's radar certification, calibration, etc. Search for the post and see if you can use it.

 

Ares' post is correct, but you may have one thing going for you. Yes, the car is capable of 40 mph in 100 feet, but this is with a professional driver at maximum acceleration.

Were you fully floored after doing a clutch-drop launch? Probably not. The cop would know if he were sitting only 100 ft away. Will he testify that he saw you do this?

 

if your coming off a turn, you couldnt have done a clutch drop. but I have thought of this defense before, but sadly I far underestimated the distances, and 100feet is a VERY short distance. even 500feet is short.

your case would more be based on a 5-40 time, becuase you cant launch the car around a turn.

but you cant find that number in a magazine, and how can you replicate it to a degree that they will believe you were really trying, and where would you try it? cant go back and see how quick you can get the car up to by the time you pass the street.

you could try the defense where a speed limit must be posted or else it goes to default speed limits depending on the road layout. but the layouts are pretty conservative. 30 is the default speed I think for most roads, unless its a school zone or something, these all vary state by state.

 

http://physics.webplasma.com/physicstoc.html

Here's a website that has the formulas to figure out distance, velocity, acceleration. The thing is that these simple formulas only hold true for CONSTANT acceleration. The figures in previous posts indicate that the acceleration is decreasing. There are formulas for varying acceleration, but those are calculus-based. You would be better off using the latter as it will be in your favor.

 

you dont need to prove how fast you could possibly going, this is what the calculus equations would provide you with.

you just need to provide how far it takes to get to 40mph. and since you know how long it take over all, it doesnt matter at what point you hit 20mph in there, or when you hit 30mph, just when you hit 40.

so constant formulas are fine.

but sadly they indicate that unless the road is less than 99.7feet from where you turned you will not benifit much from this case. you could walk in and start spouting off how you couldnt launch the car ect, but you would need a very solid case to really prove the point your trying to make, and quibling over how you launched the car isnt gonna put a smile on the judges face.

 

You are assuming that his average speed is 20mph over the 3.4 second span to get that 99.7 feet distance, correct? Wouldn't it be slightly higher, due to a slower acceleration in the "top end"? Wouldn't a more realistic average speed be like 24mph?

 

Just to put all of the math aside for a moment. There is no way of claiming that you weren't going 25mph. All you are looking for is a way to knock it down to a lower level violation. I have been to court a few times, and both times if you are within 1-3 mph of the higher level (40mph) they will almost alway knock it down to a 25-39mph violation. If you go in there trying to present all this evidence they might not appreciate it and just give you the higher penalty. Just be polite and respectful and ask to take the lower penalty.

 

Guys,
Thanks for the help and advice. I rechecked the 'crime scene' last night when I went to my friend's house in the area. The distance is much further than I remembered. When the cop first pulled me over and said I was doing 40, I immediately pleaded to give me a break and cut it down to under 40, because then I'd be able to knock it down again in court to a no points violation. The guy was a complete jerk though, and wrote it for 40. That means when it gets knocked down, i'm still gonna have 2 points.

I'd really rather get no points, and pay the higher fine...will save me money in the end.

 

Here is the answer:

Distance = velocity(starting)*time + .5 * acceleration * time * time

Hence, if it takes 3.5 seconds to 40 mph at full throttle, assuming full throttle is .7g or 6.86 meters/sec/sec, your distane to 40 mph will be 40.915 meters, or 134.2012 feet. The cop can't argue with physics. Measure exactly how far his trap was from your starting position and you will have him.

Furthermore, this calculation assumes perfect traction and delivery of energy to the pavement. That just doesn't occur. Friction plays a major part in this calculation and we are completely neglecting it. So I think you could safely add 30 feet to that calculation.

Beyond even THAT, you can add that you have to perform a shift between reaching that speed, and during the shift time acceleration is negative.

Even FURTHER, you can argue that acceleration is constantly decreasing due to gearing and wind resistance.

After that argument I think you could present them with 225 - 250 feet to 40 mph.

Does anyone agree?