Thread: Question: Accelarating speed and distance covered.

Your assistance is required for an upcoming court case.

Story
A traffic officer started giving chase to a vehicle passing at high speed.
Several kiliometers further, the traffic officer managed to catch up with the alleged speeding vehicle.
The defendant claims that it is a case of mistaken identity. The traffic officer claims that he never lost
sight of the speeding vehicle (despite several bends, hills and rises in the road). We require an answer
and mathematical formula to deteremine the distance the traffic officer covered when he reached his
top speed. This distance against other evidence (bends, uphill rises and downhills of the road) will allow
us to proof that the traffic officer did indeed lose sight of the speeding vehicle.

Situation
The traffic officer was initially driving at a speed of 80 Kilometers p/Hour.
When he saw the speeding vechicle he starting accelarating.
It then took him 55 seconds to reach a speed of 213 Kilometers p/Hour.

Questions
1. What distance (metric meters) did he cover by the time he reached 213 kilometers p/Hour?
2. What is the mathematical formula to this answer?

Thank you kindly!

I assume that the acceleration is constant.

One approach, you can draw a velocity-time graph. The distance traveled is the area under this curve. The formula for the curve is the formula asked for in problem 2. You must convert to meters when done.

Assuming constant acceleration means the graph is a straight line. It passes through the points (0,80) and (55, 213)

I'm a lawyer and know very little about mathematics. I need an answer and the formula to
challenge the traffic officer's evidence. I have no clue how to go about this.

Looking at the video footage again, the accelaration is not constant - the acceleration tapered off
the higher the speed became. I will FTP the video footage to our server which will give further insight.
Link to follow.

So...this is actually a real world thing? Not a math problem from some class?

Well, then that's different....very different. Finding a function to describe this situation would be very difficult. Especially given that no one here would know the road and the whole situation if described in words. Your best bet is still to assume constant acceleration and use that as an estimate. By the way, all this is very specific, suspiciously so. There happens to be video footage of this? You happen to know that the cop was at 80 km/h and sped up to 213 km/h in 55 seconds? Anyway, assuming constant acceleration, you'd cover roughly 2.2 km in that time. That is assuming ideal conditions of course, no bends or hills etc. In any case, it's going to be hard to pull off this defense. You'd need a lot of pictures, maybe video, and a lot more advanced math than is being used here. If you're going for confusing the judge, you'll probably have a shot But it just might come down to the cop's word against yours. If he says he kept you in his sights, the judge will believe him. I'd come up with a different defense. In the US it'd be different than in Munich. Depends on what the traffic laws are, and the traffic codes for roads, etc.

Originally Posted by Jhevon

.... By the way, all this is very specific, suspiciously so. There happens to be video footage of this? You happen to know that the cop was at 80 km/h and sped up to 213 km/h in 55 seconds? Anyway, assuming constant acceleration, you'd cover roughly 2.2 km in that time. That is assuming ideal conditions of course, no bends or hills etc. In any case, it's going to be hard to pull off this defense. You'd need a lot of pictures, maybe video, and a lot more advanced math than is being used here. If you're going for confusing the judge, you'll probably have a shot But it just might come down to the cop's word against yours. If he says he kept you in his sights, the judge will believe him. I'd come up with a different defense. In the US it'd be different than in Munich. Depends on what the traffic laws are, and the traffic codes for roads, etc.

Nothing suspicious aabout the above. Be assured that this is a serious and genuine matter.
The matter is currently on trial and the traffic officer gave evidence - hence the 80 Kilometers per hour.
We, the defence, are entitled to all the evidence pre-trial - hence we legally have the video footage.
The 55 seconds was derived from the footage itself.

Thank you for your constant accelaration suggestion as it is clearly a difficult calculation to do.
How accurate is your 2.2 kilometer answer?
What is the formula for your calculation?

Here is the footage if interested.