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Question Video: Analyzing the Distance-Time Graph for an Object That Changes Speed Physics

The graph shows the changes in the distance walked by a dog in a time interval of 8 seconds. At what time did the dog change its speed? Was the dog speed higher or lower before the point when its speed changed? What is the difference between the speed of the dog before and after it changed speed?

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Video Transcript

The graph shows the changes in the distance walked by a dog in a time interval of eight seconds. At what time did the dog change its speed?

The graph shown has distance on the vertical axis and time on the horizontal axis. It consists of two straight-line segments, one from zero to four seconds and another from four to eight seconds. So, the thing to recall here is that a straight line on a distance–time graph indicates constant speed. So, we have two segments in which the dog is moving with a constant speed, and the point where that changes is at a time of four seconds. So, the time in which the dog changed its speed was four seconds.

Next, we’re asked, “Was the dog speed higher or lower before the point when its speed changed?”

To answer this, we need to remember that speed is equal to the slope of a distance–time graph. The slope is higher in the first segment than it is in the second one. And therefore, the speed before the point when the speed changed was higher.

Finally, what is the difference between the speed of the dog before and after it changed speed?

To answer this, we need to calculate the slope of each of the two line segments. At the end of this first segment, the dog had covered a distance of 12 meters, and that took four seconds. So, the speed in that segment is three. And for the units, we take the units of the vertical axis divided by the units of the horizontal axis. So that’s three meters per second. By the end of the second segment, the dog had covered 20 meters, but he started at 12 meters, so the distance is 20 minus 12. And the time is eight seconds at the end of the segment minus four seconds at the start.

So, we have 20 minus 12, which is eight, divided by eight minus four, which is four. So, the speed in the second segment is eight divided by four, which is two. And again, that’s meters per second. So, the difference between the speed of the dog before and after it changed speed is three minus two equals one meter per second.

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