Math Problem Statement
The speed, in miles per hour, of a race car on a track is modeled by the linear function v(t)=60+1.2t, where t is the number of seconds since the car began its second lap around the track.
Solution
The function models the speed of a race car in miles per hour, where is the time in seconds since the car started its second lap.
Key Points:
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Initial Speed: At , the speed is:
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Rate of Change: The term indicates that the speed increases by 1.2 miles per hour for each second that passes.
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Speed After Time: To find the speed at any time , simply plug in the value of into the function. For example:
- At seconds:
- At seconds:
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Maximizing Speed: The function is linear, meaning there is no maximum speed as increases; the speed continues to increase indefinitely.
Questions for Further Exploration:
- What is the speed of the car after 5 minutes?
- How long will it take for the car to reach a speed of 100 mph?
- What would the speed be if the car maintained this rate for 1 hour?
- How does this model compare to a constant speed model?
- Can you describe how this model could be used to predict lap times?
Tip:
Always remember that in linear models, the slope indicates the rate of change, and the y-intercept represents the initial value.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Rate of Change
Speed and Time
Formulas
v(t) = 60 + 1.2t
Theorems
Linear Function Properties
Suitable Grade Level
Grades 8-10
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