The graph shows the position of a car over a 10-second time interval. Which of the following is the correct interpretation of the graph for the interval 1 to 3 seconds?
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A
The car remains in the same position.
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B
The car is traveling at a speed of 5 m/s.
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C
The car is traveling up a hill.
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D
The car is traveling at 5 mph.
The car is traveling at a speed of 5 m/s between 1 and 3 seconds because the graph shows a straight-line increase in position with a constant slope, indicating uniform motion at a constant rate of change of position over time.
From the graph, the car’s position increases from 0 meters at 0 seconds to 30 meters at 6 seconds. This represents a constant rate of change, meaning the car is moving at a steady speed. Dividing the total change in position by the total change in time (30 meters ÷ 6 seconds) gives a speed of 5 meters per second, which applies to any sub-interval within that linear segment, including from 1 to 3 seconds.
A. The car remains in the same position.
If the car remained in the same position, the graph would show a horizontal line, indicating no change in position over time. However, during the interval from 1 to 3 seconds, the graph clearly slopes upward, showing that the position is increasing. This confirms the car is moving, not stationary.
B. The car is traveling at a speed of 5 m/s.
This option correctly matches the slope of the graph. The straight, upward-sloping line indicates constant speed, and calculating the slope of the position–time graph confirms a speed of 5 meters per second. This interpretation aligns precisely with the visual data presented.
C. The car is traveling up a hill.
The graph represents position versus time, not elevation versus distance or time. There is no information about changes in height or terrain. Therefore, no conclusion can be drawn about whether the car is traveling uphill or downhill.
D. The car is traveling at 5 mph.
The graph uses meters for position and seconds for time, so the speed must be expressed in meters per second, not miles per hour. Additionally, 5 mph is not equivalent to 5 m/s, making this option both unit-inconsistent and numerically incorrect.
Conclusion
The interval from 1 to 3 seconds lies within the straight-line portion of the position–time graph, where position increases uniformly with time. This constant slope represents a constant speed of 5 meters per second. Careful interpretation of the graph’s units and slope confirms that option B provides the correct and most accurate description of the car’s motion during that interval.