Math Problem Statement
Suppose you leave your dorm at 8:30 am to walk to your math class, and that your entire walk is along a straight road. Ten minutes into your walk, you run into a friend and stop to chat with her for 5 minutes. Then you walk the rest of the way to class, arriving at 8:58 am. (a) Assuming you walk at a constant rate of 100 ft per minute, carefully sketch a graph of your position function, representing your distance from your house as a function of the time, t, in minutes after 8:30 am. (Be sure to label your axes!) (b) Using the graph you drew in part (a) for reference, answer the questions below. Remember to include units in your answers. i. What was your displacement over the time interval [0, 28]? ii. What was your total distance traveled over the time interval [0, 28]? iii. What was your average velocity over the time interval [0, 28]? iv. What was your average speed over the time interval [0, 28]?
Solution
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Math Problem Analysis
Mathematical Concepts
Position function
Displacement
Distance traveled
Velocity
Speed
Formulas
Displacement = final position - initial position
Total distance traveled = sum of all distances walked
Average velocity = displacement / total time
Average speed = total distance traveled / total time
Theorems
-
Suitable Grade Level
Grades 9-12
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