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:http://www.allpar.com/squads/police-…)
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: http://www.engineeringtoolbox.com/car-accelerati…
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?