Equations for pacing cars

scottfriend

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Jul 18, 2006
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I am hoping to get some help with the following problem. A police car is travelling north on Alpha Road and passes two cars that are travelling south on the same road. The police car turns around and begins to travel south and observes the two vehicles that had been traveling south turn west onto Beta Road. The second vehicle gets in the inside lane (on Beta Road), accelerates rapidly and passes the first vehicle which is in the outside lane. The police car turns west onto Beta Road and catches up with the speeding second vehicle and paces it for 300 yards at 60 m.p.h. (the speed limit is 50). The speeding driver is stopped at the one mile mark, meaning the police officer activated his lights prior to the one mile mark.

My question is what are the equations and/or parameters to figure out how fast the police officer had to go to catch up to the speeding car and pace it for the requisite distance before making the stop? I realize there are several variables not yet quantified, and consequently, there will be a range of answers. Thank you for any help or guidance with this/these equation(s).
 
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