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Composition Setup
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Excerpt
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Police car with constant acceleration must catch speeder with constant velocity.
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.
Composition Setup
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Part A
Part A
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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
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Systems:
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There are two separate systems here. Both the police car and the speeder's car will be treated as point particles.
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Interactions:
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The police car experiences a constant acceleration as a result of the action of the pavement against its wheels.
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Models:
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The motion of the speeder's car will be modeled as One-Dimensional Motion with Constant Velocity. The motion of the police car will be modeled as One-Dimensional Motion with Constant Acceleration.
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Approach:
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Part B
Part B
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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.
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Approach:
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Part B
Part B
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Wiki Markup
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