A commuter is driving a car along a straight road at a constant speed of 21.0 m/s. Just as she passes a law officer parked along the side of the road, the officer starts to accelerate 0.50 m/s2 to overtake her. Assume that the officer maintains this?

Complete Question:

Upon searching online, the full part of the question contains these two parts:

(a) determine the time it takes the police officer to reach the commuter.

Find (b) the speed and (c) the total displacement of the officer as he overtakes the commuter.

a) 84 seconds

b) 42 m/s

c) 1764 m

Explanation:

a) To find the time taken for the police officer to reach the commuter, we need to set their distance traveled 's' to be equal.

Now we can solve the following two equations for the officer and commuter:

  (for the officer as his initial speed u = 0 m/s)

(for the commuter, as her initial speed is given but acceleration is 0 m/s^2)

As s is equal we can solve these equations in the following way for the time:

thus the time taken is 84 seconds.

b) Speed of officer = acceleration * time taken to overtake commuter

   Speed of officer = 0.5 * 84 = 42 m/s

c) Total displacement = 0.5 * a * (t^2)

   Total displacement = 0.5 * 0.5 * (84^2)

   Total displacement = 1764 m

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