Question Video: Determining the Speed of an Object from a Distance-Time Graph Science

Video Transcript

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

Here, we’ve been given a distance–time graph of an object in motion and we want to find the speed of this object. So let’s begin by taking a closer look at the graph. We can see that the vertical axis shows the distance the object travels in meters and the horizontal axis shows the time that the object has been traveling for in seconds. Now, to answer this question, let’s recall that the speed represented by a straight line on a distance–time graph is equal to the gradient of the line. The gradient of a line is always measured between two points. And since this object has a constant speed, the line on the graph has a constant gradient. So we can choose to measure the gradient between any two points along this line.

Here, we’ll choose these two points marked in pink. Now, the gradient of a line on a distance–time graph, and therefore the speed of the object whose motion the line represents, is equal to the change in distance divided by the change in time between the two points that we’ve chosen. First, let’s find the change in distance between the points. We can see that this point here corresponds to a distance of zero meters and this point here corresponds to a distance of six meters. Therefore, the change in distance between these two points is equal to six meters minus zero meters, which is just equal to six meters.

Now, let’s find the change in time between the two points. We can see that this point here corresponds to a time of zero seconds and this point corresponds to a time of three seconds. So the change in time between these two points equals three seconds minus zero seconds, or just three seconds.

Now that we’ve determined the change in distance traveled and the change in time between the two points on the line, we can calculate the speed of the object. So, substituting these values into the formula for speed, we have six meters divided by three seconds. Six divided by three simplifies to two, and we’re working in units of meters per second. So we have our final answer. The speed of the object represented by the line on the distance–time graph is two meters per second.