Math Problem Statement
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A car accelerates from 12 m/s to 25 m/s in 6.0 s. What was its acceleration? How far did it travel in this time?
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A car slows down from 20 m/s to rest in a distance of 85 meters. What was its acceleration?
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Ando traveling 50 m/s passes a stationary police officer. The police officer immediately begins pursuit at a constant acceleration of 5 m/s2. a) How much time will it take the officer to reach Ando, assuming that Ando maintains a constant speed? b) How fast will the police officer be traveling at this time?
Solution
Let's tackle each problem one by one.
1. Car acceleration and distance traveled
Given:
- Initial velocity () = 12 m/s
- Final velocity () = 25 m/s
- Time () = 6.0 s
Acceleration ()
The formula to calculate acceleration is:
Substitute the given values:
Distance traveled ()
The formula to calculate distance when initial and final velocities, and time are known is:
Substitute the known values:
2. Car deceleration
Given:
- Initial velocity () = 20 m/s
- Final velocity () = 0 m/s (since the car comes to rest)
- Distance () = 85 m
Acceleration ()
The formula to calculate acceleration when initial velocity, final velocity, and distance are known is: Rearrange to solve for :
Substitute the known values:
3. Police pursuit problem
Given:
- Ando's speed () = 50 m/s
- Police officer's acceleration () = 5 m/s
(a) Time for the officer to reach Ando
The distance traveled by Ando () in time is:
The distance traveled by the police officer () in time is:
When the officer reaches Ando, these distances are equal:
(b) Speed of the police officer at this time
The final velocity () of the police officer can be calculated using: Since the initial velocity () of the officer is 0,
Summary
- Acceleration: Distance traveled:
- Deceleration:
- Time for officer to reach Ando: Speed of officer at this time:
Would you like more details or have any questions about these solutions?
Related Questions:
- What is the formula for calculating acceleration?
- How do you calculate the distance traveled when acceleration is constant?
- How does initial velocity affect the distance traveled under constant acceleration?
- What are the different equations of motion for uniformly accelerated motion?
- How can you calculate deceleration if you know the distance and initial velocity?
- What is the relationship between velocity and time under constant acceleration?
- How do you determine the time it takes for two objects with different accelerations to meet?
- How do you calculate final velocity under constant acceleration?
Tip: Always keep track of units and ensure consistency throughout your calculations to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Uniform Accelerated Motion
Deceleration
Formulas
Acceleration: a = (v - u) / t
Distance: s = ut + (1/2)at^2
Final Velocity: v = u + at
Theorems
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Suitable Grade Level
High School
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