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Question Video: Interpreting Horizontal Lines on Speed-Time Graphs Science

Which of the following corresponds to a horizontal line on a speed–time graph? [A] An object that travels in a horizontal direction [B] An object at rest [C] An object that travels at any constant speed

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Video Transcript

Which of the following corresponds to a horizontal line on a speed–time graph? Is it (A) an object that travels in a horizontal direction, (B) an object at rest, or (C) an object that travels at any constant speed?

Let us consider a pair of axes for a speed–time graph where the horizontal axis represents time and the vertical axis represents speed. We can add a horizontal line to this graph, for example, a line that represents a speed, equal to three meters per second. We can see that for increasing values of time shown along the horizontal axis, the value of speed shown on the vertical axis is a constant three meters per second, neither increasing nor decreasing. The only thing that this line shows is that the object that has had its motion represented by the graph travels a distance of three meters in each one-second time interval shown on the graph.

The direction in which the object travels three meters in any particular time interval is not something that the graph can show. A distance can be traveled in any direction, even changing directions. The fact the line on the graph is horizontal does not mean that the object has horizontal motion. This is because a line on a speed–time graph does not show the shape of the path that the object travels along.

We can see that option (A) cannot be correct. Option (A) says that the graph shows that an object travels in a horizontal direction. But the graph does not show anything about the direction of motion of the object.

Option (B) says that a horizontal line on a speed–time graph shows an object that is at rest, meaning an object that does not move. An object that does not move does not change the distance that it travels. Option (B) might then seem correct because a horizontal line on the graph shows a value on the 𝑦-axis of the graph that does not change.

Let us consider again the example of the horizontal line with a constant value for speed of three meters per second. The object that has motion represented by this line moves three meters in each one-second time interval shown on the graph. An object that is at rest would have to travel zero distance in a time interval, not a distance of three meters. We could replace the horizontal line with a constant value for speed of three meters per second with a horizontal line with a constant value for speed of zero meters per second. This would represent an object that is not moving. We can see then that there is one particular horizontal line that represents an object at rest, but all other horizontal lines do not represent an object at rest.

Option (C) says that a horizontal line on a speed–time graph shows an object that travels at a constant speed. We have seen that a horizontal line on a speed–time graph can show a constant speed of three meters per second. And we have also seen that a horizontal line on a speed–time graph can show a constant speed of zero meters per second. A horizontal line on a speed–time graph can in fact show any constant speed. Whatever the vertical axis value of the line is on a speed–time graph is the constant speed shown by the line, so option (C) is correct.

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