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Question Video: Using a Distance–Time Graph to Calculate the Speed of an Object Science

The distance–time graph shows an object moving at a uniform speed. What is the speed of the object?

02:20

Video Transcript

The distance–time graph shows an object moving at a uniform speed. What is the speed of the object? (A) Nine meters per second, (B) 2.5 meters per second, (C) 21 meters per second, (D) 90 meters per second.

In this question, we are asked to find the speed of the object shown in the distance–time graph.

To find the speed, we just have to find the gradient of the graph. This is because the gradient of a graph is the change in the 𝑦-axis over the change in the 𝑥-axis, which in the case of this graph would be the change in distance over the change in time. And distance over time is just speed. This can be written as 𝑉 equals Δ𝑑 over Δ𝑡, where 𝑉 is the speed, Δ𝑑 is the change in distance, and Δ𝑡 is the change in time. So, we calculate the speed of the object by dividing the distance the object has traveled by the time it takes to move that distance.

Looking at the distance axis, we see that the units start at zero meters, then the first marking is at three meters, the second at six, and so on. The distance increases by three meters for each marking. We note this because the end of the line doesn’t have a marking. It’s just one above 12. This means that the distance traveled must be three meters more than 12, so 15 meters. This gives us the change in distance.

Now let’s look at time. For the time axis, we see that the units start at zero seconds, the first marking is at two seconds, the second at four, and so on. The time increases by two seconds for each marking. And the end of the line matches up with the third marking, indicating that the change in time is six seconds. This means that each 15-meter increase in distance corresponds to a six-second increase in time. Substituting these values into our equation for speed, we see that the speed is equal to 15 meters per six seconds.

All of the possible answer choices here are whole numbers or decimals, so let’s simplify our expression. 15 divided by six is equal to 2.5. The units of speed for this graph are meters per second. This means that the speed of the object given by this distance–time graph is 2.5 meters per second. The correct answer is option (B).

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