How is constant speed shown on a graph

The principle of slope can be used to extract relevant motion characteristics from a position vs. As the slope goes, so goes the velocity. Consider the graphs below as another application of this principle of slope. The graph on the left is representative of an object that is moving with a negative velocity as denoted by the negative slope , a constant velocity as denoted by the constant slope and a small velocity as denoted by the small slope. The graph on the right has similar features - there is a constant, negative velocity as denoted by the constant, negative slope.

Once more, this larger slope is indicative of a larger velocity. As a final application of this principle of slope, consider the two graphs below. Both graphs show plotted points forming a curved line. Curved lines have changing slope; they may start with a very small slope and begin curving sharply either upwards or downwards towards a large slope.

In either case, the curved line of changing slope is a sign of accelerated motion i. Applying the principle of slope to the graph on the left, one would conclude that the object depicted by the graph is moving with a negative velocity since the slope is negative. Furthermore, the object is starting with a small velocity the slope starts out with a small slope and finishes with a large velocity the slope becomes large.

That would mean that this object is moving in the negative direction and speeding up the small velocity turns into a larger velocity. This is an example of negative acceleration - moving in the negative direction and speeding up. The graph on the right also depicts an object with negative velocity since there is a negative slope. The object begins with a high velocity the slope is initially large and finishes with a small velocity since the slope becomes smaller.

So this object is moving in the negative direction and slowing down. This is an example of positive acceleration.

Perhaps the objects moved different distances before the start time of the measurements taken for the graph. For our purposes, it does not matter what the value of distance is; in all three cases, the distance does not change during the measurement period.

Therefore, all three objects would have identical speed—time graphs. Specifically, the speed—time graph for each of the objects would look like this:. This graph shows an object whose distance increases at a constant rate.

We can see this as follows. In the diagram below, we have the same graph, but now we have highlighted two triangles. The hypotenuse of both triangles lies along the line plotted on the distance—time graph. The horizontal and vertical sides of the red-dashed triangle each have a side length of 1. For the horizontal side, this is in units of seconds , while for the vertical side, it is in units of metres. What this triangle is telling us is that the object travels a distance of 1 m the first 1 s shown on the graph.

Now looking at the blue triangle, we see that the vertical and horizontal sides each have a side length of 2. This tells us that the object travels a total distance of 2 m in the first 2 s. The sides of the blue triangle are in the same proportion as the sides of the red triangle. In fact, no matter where we draw a triangle, so long as its hypotenuse lies along the line on the graph, we will find that the horizontal and vertical sides of the triangle are in this same proportion.

This shows that the object travels equal distances in equal times. We may recall that if an object moves equal distances in equal times, then that object moves with a constant speed. By drawing two triangles in the way we have shown, it is straightforward to verify that the horizontal and vertical sides of the triangles will be in the same proportion for any distance—time graph where the distance increases with time as a straight line.

In other words, all distance—time graphs that show a straight line represent motion at a constant speed. Therefore, the corresponding speed—time graph will always be a horizontal line.

The steeper a line is on a distance—time graph, the greater the distance moved by the object in each unit of time. We can also recall that the greater the distance moved per unit time, the greater the speed of an object. Therefore, we can see that the steeper the line on a distance—time graph is, the higher up the corresponding horizontal line will be on a speed—time graph.

Each color line on the distance—time graph corresponds to the same color line on the speed—time graph. On the distance—time graph, the red line is the least steep. Therefore, this line shows the smallest speed. The smallest speed is represented by the lowest horizontal line on the speed—time graph. Similarly, the blue line on the distance—time graph is the steepest.

Therefore, it corresponds to the highest horizontal line on the speed—time graph. Meanwhile, the green line lies between these two. Which color line on the speed—time graph shows the motion of the object on the distance—time graph? In this question, we are presented with a distance—time graph along with a speed—time graph. We are asked to identify which of the two lines on the speed—time graph shows the motion of the object on the distance—time graph.

Looking at the distance—time graph, we see that this graph shows a straight line. The distance increases in equal proportion to the time, which means that the object travels equal distances in equal times.

Therefore, we know that the distance—time graph shows the motion of an object that moves at a constant speed. If we now look at the speed—time graph, we have two potential choices. We need to work out whether it is the green line or the red line that represents motion at a constant speed. The red line shows speed increasing as time increases. Since the speed is increasing, it cannot be constant. So the red line cannot represent the motion at a constant speed shown in the distance—time graph.

The green line on the speed—time graph is a horizontal line. This shows that the speed of the object has the same value for all values of time. Therefore, the speed of that object is not changing; or, in other words, this green line shows motion at a constant speed. So, our answer to the question is that it is the green line on the speed—time graph that shows the motion of the object on the distance—time graph. Speed-time graphs are very useful when describing the movement of an object.

We can use them to determine whether or not the object is moving at any point in time. We can also use them to see what speed the object is travelling at that point in time. Using data from the graph, we can calculate any acceleration , the change in speed and the change in time. We can also use graphs to calculate distance travelled. The area under a speed-time graph represents the distance travelled. This is a velocity time graph of an object moving in a straight line due North. The displacement of this object is the area of the velocity time graph.