Comment:
Migration of unmigrated content due to installation of a new plugin
Composition Setup
Excerpt
hidden
true
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.
Deck of Cards
id
partdeck
Card
label
Part A
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
Toggle Cloak
id
sysa
Systems:
Cloak
id
sysa
There are two separate systems here. Both the police car and the speeder's car will be treated as point particles.
Toggle Cloak
id
inta
Interactions:
Cloak
id
inta
The police car experiences a constant acceleration as a result of the action of the pavement against its wheels.
Toggle Cloak
id
moda
Models:
Cloak
id
moda
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.
Toggle Cloak
id
appa
Approach:
Cloak
id
appa
Card
label
Part B
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.
