Help Needed: Calculating Acceleration over 185 Meters

[wrist]

Hi, I'm after some help because my intelligence doesn't stretch as far as you guys!
I am being taken to court for speeding, the police officer has stated in her evidence that she saw me traveling at 80 mph, that at that time she was traveling at 70 mph. She then states that both she and I were traveling at 120-130 mph by the time we passed a bridge which is 185 meters from where she first saw me.
My question is, if I accelerated from 80 mph to 120 mph in a distance of 185 meters (and she accelerated from 70mph to the same speed) what was the time taken to travel that distance (obviously I want to prove that our vehicles were not capable of what she states). I understand that any calculation would presume constant acceleration but that's the best I can hope for.
Thanks

 

[TVP45]

The formula you are probably looking for is
V^2 = Vo^2 + 2a(X-Xo)
where V is the final velocity (120 mph or about 180 ft/s)
Vo is the initial velocity (80 mph or about 75 ft/s)
X-Xo is the distance traveled (185 m or about 600 ft)
a is the acceleration needed.
An ordinary car might accelerate at about 10 or 12 ft/s^2 maximum. What were you driving?

If you want to do the time, use
t = 2(X-Xo)/(V+Vo)

Good luck finding a judge who can do algebra.

 

[Mech_Engineer]

That sounds REALLY fast to me... going 80-120mph in 185m equates to 4.1 seconds, assuming constant acceleration.

To put that into perspective, the Saleen S7 Twin Turbo with 750 horsepower takes about 3.7 sec to go from 80 to 120, and the regular S7 takes about 4.3 sec I think, with 550 hp.

You would have had to be driving a VERY fast car.

 

[berkeman]

wrist didn't say car, s/he said "vehicle". I'd guess both vehicles were motorcycles, and yes, that is not difficult for a production motorcyle.

 

[berkeman]

And BTW, if those speeds are correct, wrist is going to court for "fleeing and eluding", not speeding...

 

[rcgldr]

If it was a motorcycle, it depends on the motorcycle. If the police bike was a Harley or a BMW, it wouldn't be that fast. The Harley can't go 120mph at all, and I'm not sure that a BMW could either with the big fairing. If it was a Kawaski 1000, seems possible.

Also, with a 10mph head start, if the tracking cop is trying to reclose the initial gap, then they have to accelerate faster or longer in order to catch up and close the gap, and their speed will be significantly more than the vehicle being tracked when the gap closes.

As far as "fleeing..." goes, it depends on the state (or country), and it would have been written on the ticket.

As far at the the "judge knowing algebra ..." he doesn't have to. You can present a simple statement that it wouldn't be possible to go from 80 to 120 in 4.1 seconds, and it's up to the cop to counter this, not the judge.

 

[wrist]

thanks

Hi, thanks for the replies, it's in the UK so no fleeing and evading! I was on a ktm supermoto which does accelerate quickly (debatable if THAT quickly) but her claim is tha her fully laden diesel skoda octavia VRS estate went from 70mph to 120mph withinthe 185m which is impossible.

 

[rcgldr]

Hi, thanks for the replies, it's in the UK so no fleeing and evading! I was on a ktm supermoto which does accelerate quickly (debatable if THAT quickly) but her claim is tha her fully laden diesel skoda octavia VRS estate went from 70mph to 120mph withinthe 185m which is impossible.

Obviously her car didn't accerlate that fast so she was "guestimating" your speed. I don't know what the UK laws are concerning police "guestimates" of another vehicle.

Assuming that you have the 950 KTM Supermoto with 98 hp, and it's semi-faired body work, 80mph to 120mph in 4.13 seconds seems pretty fast. Or is it the 990 KTM Superduke with 118hp?

ktm_950_supermoto_2007.php

ktm_990_super_duke_2007.php

 

[rbj]

unfortunately, without getting (and paying for) an "expert witness" with credentials (like a Ph.D. in physics or mechanical engineering and teaching at some university) that the judge will recognize, and this expert witness will digest the quantiative physical evidence (or just the ridiculous numbers that the cop was spouting) and present to the judge that their expert conclusion is that the cop's story is beyond reasonableness physically, you cannot expect the stupid-ass judge to be able to do the math and come to a reasonable conclusion him or herself. he or she will just take the word of whatever authority he or she recognizes that testifies. if there is a conflict in testimony of expert authorities, then the judge (or jury) will have to think a little and decide which expert witness they want to believe.

 

[rcgldr]

unfortunately, without getting (and paying for) an "expert witness" with credentials

In the USA, while monitoring traffic court for a class, expert witnesses weren't required. I remember one case where a motorcyclist was clocked at 60mph via radar 1/10th of a mile before stopping and making right turn. In court the motorcyclist simply stated that the distance (503 feet) was too short for this to happen. Since the officer couldn't offer an explanation that it was possilbe, the charge was dismissed. While watching this, I did a mental calculation, on a crotch rocket, 60mph to 0mph can take as little as 3 seconds, with an average speed of 44 feet per second, that's 132 feet to stop. That would have given the motorcycle 371 feet, or a bit over 4 seconds to be going 60mph before hitting the brakes. However since the officer wasn't trained in basic braking distance physics, the guy's charge was dismissed.

A somewhat infamouse case involved an aircraft cop using two stopwatches to clock 2 motorcycles going at high speed over a 1/4 mile distance. The cop claimed one of the bikes to be going 205mph (4.4 seconds), and the other at 150mph or less. Clearly the cop switched the bikes while clocking them or started a stop watch early or stopped one early, however the cop refused to admint a mistake and insisted the bike was going 205mph. The bike claimed to be going 205mph was a Honda 1000cc V-Twin VFR with around 100hp stock. The bike had intake and modified exhaust, but for this bike to reach 200mph it would have needed over 200hp, something only possible with a turbo-charger, which the bike didn't have. If I remember correctly, in that state, the actual speed didn't matter, and the cost of the ticket was less than $300. For comparason, in California, a typical speeding ticket for 75mph on a 65mph freeway costs over $400.

 

[brewnog]

So how fast were you going?

Be a man and take the points!

Then again, if she is using that impossible statement in court, you've probably got a pretty good chance of getting let off. See www.pepipoo.com

 

[Garen]

This seems like some homework problem that you're just trying to get the answer for.

 

[wrist]

hmmm

Thanks again. In answer to some of your questions :
its the supermoto 950 and when dyno tested mine put out 93bhp,
Sadly no its not just homework!
I will get my solicitor to present the facts ie 70 mph =32 meters per second=5.78 sec to travel 185 meters and 120mph =54 meters per second=3.43 sec to travel 185m and an average would be 4.1 seconds (none of the above are possible in her skoda!)

 

[JonWhitehouse]

Anyway, in the UK, max speed allowed anywhere is 70mph, so provided you were accelerating away from her at some point and she was at a constant 70mph, you would be speeding anyway.

 

[Kurdt]

Anyway, in the UK, max speed allowed anywhere is 70mph,

Well that's not strictly true. I doubt this occurred on the isle of man though.

Either way I doubt you will be successful, wrist, in opposing the traffic policewoman's claims.

 

[brewnog]

Well that's not strictly true. I doubt this occurred on the isle of man though.

Aha, but the Isle of Man isn't in the United Kingdom! It's a Crown Dependency!

 

[Kurdt]

Aha, but the Isle of Man isn't in the United Kingdom! It's a Crown Dependency!

Damn, and I'd have gotten away with it too if it weren't for you pesky kids.