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A common type of kinematics problem involves one person or object catching up to another person or object. Here we illustrate a few typical variations of this problem.

Part A

A speeder driving with a constant speed of 24.5 m/s approaches a (hidden) stationary police car on a long, straight road. The police officer detects the speeder using radar, and so the instant the speeder passes the police car, it begins accelerating after the speeder at a rate of 5.00 m/s2. How long will it take for the police car to catch up to the speeder from the instant its acceleration begins?

Solution

Systems:

There are two separate systems here. Both the police car and the speeder's car will be treated as point particles.



Interactions:


Models:


Approach:

Part B

Again, a speeder driving with a constant speed of 24.5 m/s approaches a (hidden) stationary police car on a long, straight road. The police officer detects the speeder using radar, but this time the police officer begins accelerating at a rate of 5.00 m/s2 only after the speeder has progressed 100 m down the road (the speeder has a 100 m head start). How long will it take for the police car to catch up to the speeder from the instant its acceleration begins?

Solution

Systems, Interactions and Models: The same as for Part A.

Approach:

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[Examples from Kinematics]

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