Question
Describing Motion Directions: The distance-time graph below shows the motion of a student walking to a convenience store for a loaf of bread and returning home Use the graph to answer questions 1 through 5. 1. In which segment was the student moving at the slowest rate of speed? __ 2. Which segment indicates that the student might be stopped at the convenience store? __ 3. In which two segments was the student moving at the fastest rate of speed? __ 4. In which segment might the student be waiting for a traffic light? __ 5. Which took longer walking to the store or walking home? __
Answer
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Haf
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Answer
To answer these questions, we need to analyze the given information about the displacement-time graph and use the slopes of the segments to infer the speed of the student at different times.1. In which segment was the student moving at the slowest rate of speed?The rate of speed is indicated by the slope of the line on a displacement-time graph. The segment with the gentlest slope (least steep) represents the slowest rate of speed. From the given coordinates, we can calculate the slopes of segments a, b, c, and d by dividing the change in displacement by the change in time for each segment.- Segment a: From the start to (3,15), the slope is 15/3 = 5 units of displacement per unit of time.- Segment b: From (3,15) to (9,15), the slope is 0 because the displacement does not change, indicating the student is stopped.- Segment c: From (9,15) to (13,0), the slope is (0-15)/(13-9) = -15/4 = -3.75 units of displacement per unit of time.- Segment d: From (13,0) to (15,0), the slope is 0 because the displacement does not change, indicating the student is stopped again.The slowest rate of speed is indicated by the smallest absolute value of the slope, which is 0 in segments b and d, where the student is stopped. However, if we consider only the segments where the student is moving, the slowest rate of speed is in segment c, with a slope of -3.75.Answer: Segment c (if considering movement) or segments b and d (if considering stops).2. Which segment indicates that the student might be stopped at the convenience store?A segment where the student might be stopped would have a slope of 0, indicating no change in displacement over time.Answer: Segment b, where the displacement remains constant at 15 units.3. In which two segments was the student moving at the fastest rate of speed?The fastest rate of speed is indicated by the steepest slope. Since we have already calculated the slopes, we can see that segment a has a slope of 5, and segment c has a slope of -3.75 (in absolute value, 3.75).Answer: Segment a and segment c have the steepest slopes, indicating the fastest rates of speed.4. In which segment might the student be waiting for a traffic light?A segment where the student might be waiting for a traffic light would show a temporary stop or a period of no displacement. This would be indicated by a slope of 0.Answer: Segment d, where the displacement remains constant at 0 units.5. Which took longer, walking to the store or walking home?To determine which took longer, we need to look at the time intervals for each journey.- Walking to the store: From the start to the convenience store is from the start to segment b, which is from time 0 to time 9.- Walking home: From the convenience store to home is from segment b to the end of segment e, which is from time 9 to time 15.Answer: Walking to the store took 9 units of time, and walking home took 6 units of time. Therefore, walking to the store took longer.