4) A police officer hidden at an intersection observes a car that ignores a stop

Question

4) A police officer hidden at an intersection observes a car that ignores a stop sign, crosses the intersection, and continues on at a constant speed. The police officer takes off in pursuit as soon as it passed the stop sign, accelerating at 6.2m/s/s until her speed is 80m/s, and continues at this speed until she catches the car. (so there are two parts of the cop’s motion which add up)

The police officer catches the car at a total distance of 1.4km from the intersection.

How fast was the car traveling? How long does it take to catch the car?

Explanation / Answer

Let

T = time required for the speeder to negotiate 1400 m (or 1.4 km)
speed = 80 m/s = 3.6 km/hr
T = (1.4/3.6) * 3600 = 1400 seconds

This is also the time that the police car will take to catch up with the speeder.

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