Math Problem Statement
Solution
To determine during which time interval Riley ran the fastest, we need to calculate her speed (rate of change of distance over time) in each interval. The formula for speed is:
The two time intervals are:
- From to (interval ),
- From to (interval ).
Interval [0, 8]:
From the graph:
- At , the distance is 0 miles.
- At , the distance is 1 mile.
The speed in this interval is:
Interval [2, 11]:
From the graph:
- At , the distance is 0.4 miles.
- At , the distance is 1.5 miles.
The speed in this interval is:
Conclusion:
Riley ran faster during the time interval , as her speed was slightly higher: 0.125 miles per minute compared to 0.122 miles per minute during .
Would you like more details or have any questions?
Here are five related questions you can explore:
- What is the total distance Riley covered during her entire run?
- What was Riley's average speed over the entire run?
- Can we model Riley’s motion using a linear equation for each segment?
- How does acceleration differ from average speed in this context?
- What factors could affect Riley's running speed over different intervals?
Tip: When analyzing graphs, always look for key points that indicate changes in direction, slope, or behavior to better understand motion or other trends.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rate of Change
Distance-Time Graph
Formulas
Speed = Change in Distance / Change in Time
Theorems
-
Suitable Grade Level
Grades 6-8