Stop an Escaping Car

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.

• 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.