Sample physics problem/game for all you Opponauts:

"Atlantian" (Atlantian) 10/10/2014 at 18:05 • Filed to: None

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Hypothetically, if a cop is waiting alongside a straight road (perfectly smooth, and perfectly straight, no crests, dips, or other cars) in a Dodge Charger patrol car. (specs for a police Charger here: !!!error: Indecipherable SUB-paragraph formatting!!! )

And you are driving along at a static pace with a(t)=0 —v(t) is unknown—.

When you pass him is when he'll flip on the sirens and start accelerating flat out to catch up to you.

Part I)What initial cruising speed will guarentee that particular Charger patrol car will be useless at pursuing you to an imaginary state boarder in 10 miles?

Part II) And if you floored it (presumably in top gear, as this would be much higher than the interstate limit) in a reasonably attainable car, how low would that "escape velocity" reasonably be?

Here's some information that could help calculate rates of acceleration at certain speeds (in mph), it appears that acceleration is an inverse function to how long you've floored it: !!!error: Indecipherable SUB-paragraph formatting!!!

There is also some standard/benchmark acceleration rates of common road cars.

Part III) Now, if the Charger was pointed perpendicular to the road, or even parked facing the other way, how low can that initial "escape velocity" be?

burntartichoke > Atlantian 10/10/2014 at 18:19

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Escape velocity:

On Earth, 11.2 km/s :P

ttyymmnn > Atlantian 10/10/2014 at 18:22

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Is this going to be on the test? I have enough trouble with my 6th grader's math homework.

treesmakewater > ttyymmnn 10/10/2014 at 18:27

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There will only be problems like this in the test

Atlantian > treesmakewater 10/10/2014 at 18:44

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On the test of LIFE.

The cost of failing this test is JAIL TIME.

in VIRGINIA.

Racescort666 > Atlantian 10/10/2014 at 20:33

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It would be easier to use a tested acceleration profile for the squad car rather than trying to estimate it. Essentially, the acceleration is the torque at the wheels multiplied by the rolling radius of the tire divided by the mass of the vehicle. This gets complicated since the Charger can likely spin the tires in low gear. But you don't want to limit your frictional force with the static weight distribution in low gear because of weight transfer adding force to the rear, this also changes camber and whatnot changing your coefficient of friction with the road. Plus, we don't really know what that is to begin with. Also, air resistance starts becoming a major factor coupled with the fact that at higher gear, you have less mechanical advantage from the engine.

Regardless, there is an easier way of doing this. If you pass the cop and have 10 miles to go, you're probably going to be interested in the top speed of the cop car, 150. The 1/4 mile time for the charger is about 14.5s (pretty good). My guess is that the trap speed is around 100 mph. This is already pretty close to the top speed of 150 for the Charger. The safest bet would be to be going faster than 150. I did a little more digging and found that several R/T Challengers (basically a 2 door Charger, I guess) which does the standing mile at a speed of almost exactly 150. I have to start guessing now but you're looking at roughly 30-40 seconds to make that pass. So you take the distance you go in those 30-40 seconds and compare that to your speed vs 150.

For arguments sake, let's say it takes 35 seconds to get to 150 and that covers 1 mile. In 35 seconds at 140, you cover 1.36 miles. In that same 35 seconds, the cop has gone 1 mile and is now going 150. He only has to make up 0.36 miles (1900 ft) at a 10 mph speed difference. This takes about 130 seconds and covers a total of 5.4 miles.

Let's say you went faster, 145: you will have gone 1.41 miles and to make up that 0.41 miles, it takes the cop almost 5 minutes. Fortunately, you will have crossed the state line by then because the total distance covered is about 12.3 miles.

There would be a way to calculate it exactly but that would be an excersize in futility since it greatly depends on how quickly the cop gets to 150/the mile mark.