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

Question Video: Recognizing That on a Distance–Time Graph a Steeper Gradient Means a Greater Speed Science • Third Year of Preparatory School

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 we’re told shows the movement of an object that changes from moving at one uniform speed to moving at a different uniform speed. We are asked to look at this graph and figure out which of the colored lines represents the movement that has the greater speed. In order to figure this out, we will need to recall how to read a distance–time graph and how to use such a graph to find an object’s speed.

A distance–time graph, like its name suggests, is a graph measuring the distance that an object has traveled and the amount of time that it has traveled for. We can see that we have distance plotted on the vertical axis and time on the horizontal axis. Recall that the speed of an object is defined as the distance traveled by that object divided by the time it traveled for. This means we could find the speed of each of this object’s movements if we had the values for this graph. But even without numerical values, we can still compare the two line sections representing the two sections of movement. In particular, we are interested in the slope of the lines.

The slope of a line is defined as the change in the vertical coordinate divided by the change in the horizontal coordinate. Because the speed of an object is equal to the distance traveled divided by the time taken and because the vertical coordinate on a distance–time graph is distance and the horizontal coordinate is time, then the slope of a line on a distance–time graph gives us the speed of the object. A larger change in distance over a given change of time will correspond to a steeper slope and a greater speed.

So let’s look at the blue and red lines on this graph and compare them. Looking at the slopes of the lines, we can see that the red line is steeper than the blue line. This means that the red line represents the movement with the greater speed. Therefore, option (B), the red line, is the correct answer.

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