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Question Video: Recognizing That on a Distance–Time Graph a Steeper Gradient Means a Greater Speed Science

The distance–time graph shows an object that changes from moving at one uniform speed to moving at a different uniform speed. Which color line shows the greater speed?

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Video Transcript

The distance–time graph shows an object that changes from moving at one uniform speed to moving at a different uniform speed. Which color line shows the greater speed? (A) The blue line, (B) the red line, (C) both lines show the same speed.

In this question, we are given a distance–time graph that shows the movement of an object. The object changes speed from one uniform speed to another. This is represented with a blue line for the first uniform speed and a red line for the second uniform speed that the object has. We are asked to look at this graph and figure out which of the lines represents the movement with the greater speed.

Before we begin to figure this out, let’s remind ourselves how to read distance–time graphs and how to use them to find the speed of an object. A distance–time graph plots distance on the vertical axis against time on the horizontal axis. Let’s recall that the slope of a line is equal to the change along the vertical axis divided by the change along the horizontal axis. This means that the slopes of these lines on the distance–time graph are equal to the change in the distance traveled divided by the change in time, that is, the time taken to travel the distance.

Now, the question is asking us to figure out which line has the greater speed, so let’s define what speed is. The speed of an object is equal to the distance the object travels divided by the time taken to travel the distance. Notice that this is the same fraction that gives us the slope of a line on a distance–time graph. This means that the slope of a line on a distance–time graph is equal to the speed of the movement represented by the line. The steeper the slope of the line, the greater the speed.

So, in order to find which line represents the greater speed, we need to look at the blue line and the red line and see which one has the steeper slope. Looking at the two lines, we can see that the blue line has a steeper slope than the red line. This means that the blue line represents the movement with greater speed. So option (A), the blue line, is the correct answer.

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