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MATHEMATICS - CASE STUDY

    Introduction


Stop an Escaping Car
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In an exercise offered by a police school, the students are required to pursue a passing car using a police car.

What is known:

  • The passing car has a constant velocity of 80 mph when it passes the police car.
  • The police car's velocity can be modeled as

    where v is in mph, and t is in hour.
  • The police car starts at rest. The maximum velocity of the police car is 120 mph.
     
    Questions

 

  How long does it take the police car to catch the escaping car?
     
    Approach


 
  • Both of the cars cover the same distance when they ride side by side.The area under the velocity curves for each car will me then same.
  • Transfer the unit of velocity to miles/minute to get better graphics. Then the velocity of the passing car is 1.333 miles/minute, and the police car's velocity function is

    where v is in miles/min, and t is in minute.