How to Read Graph Showing Y Axis Speed in M/s X Axis Time in Seconds

In this explainer, nosotros volition larn how to utilise speed–fourth dimension graphs to show the speed of an object in uniform motion.

We tin recall that the speed of an object is the distance moved by that object per unit of measurement time.

Mathematically, if an object travels at a constant speed such that it moves a altitude in a time , then speed is given by

We can apply a speed–time graph to plot an object'south speed at different times.

Nosotros may recall that the horizontal axis of a graph is chosen the -axis and the vertical axis is the -centrality. A speed–fourth dimension graph measures time along the -axis, or the horizontal axis, and speed along the -centrality, or the vertical axis.

Let's look at a quick example problem in which we are asked to identify a speed–fourth dimension graph.

Example one: Identifying Which of 2 Graphs Is a Speed–Fourth dimension Graph

Which of the post-obit is a speed–time graph?

Answer

The question asks us to identify which of the 2 graphs is a speed–fourth dimension graph.

We can recall that a speed–time graph plots speed on the -axis against fourth dimension on the -axis.

Looking at graph A, nosotros meet that information technology plots distance on the -axis and fourth dimension on the -axis. Therefore, it cannot be a speed–time graph. It is, in fact, a distance–time graph.

Meanwhile, graph B does indeed plot speed on the -centrality and time on the -centrality. This means that this graph is a speed–time graph.

Our answer to the question is therefore that the graph in option B is a speed–time graph.

In the above example, nosotros take seen what the axes of a speed–time graph wait like.

Now let'southward consider how we may plot data on such a graph.

We will imagine that we take an object that moves at a constant speed. We volition further imagine that we have some ways of measuring the speed of this object at any instant in time.

Suppose that nosotros measure the object's speed in one case every second, and obtain the following measurements.

Time (south)	0	ane	2	3	iv	5
Speed (m/s)	3	3	3	3	three	3

Find that since the speed of this object was constant, the same value of speed is measured each time such a measurement is fabricated.

At present let's plot these measurements on a speed–fourth dimension graph.

We will begin with the measurement taken at a time of 0 seconds. The speed of the object at this time is 3 m/s. To plot this, nosotros look on the time axis (or -axis) for a value of 0 s. At this horizontal position, we and so go upward on the graph until we reach a pinnacle on the speed axis (or -axis) of 3 thou/south. Nosotros place a cantankerous here, where the vertical line through "time = 0 southward" intersects the horizontal line through "speed = iii m/s."

At present we will consider the next measurement, taken at a time of 1 2d. The speed of the object is, over again, 3 m/south. We await on the time axis of our graph for a value of 1 s. We so follow a vertical line upward from this position until we get to a height of 3 g/south on the speed centrality, where the horizontal line through "speed = 3 thou/s" intersects the vertical line through "time = 1 s."

Applying the same process to the remaining 4 measurements, nosotros make it at the following speed–time graph for the object.

Nosotros may draw a trend line through the points to help brand the behavior of the object articulate. In this case, all of the points prevarication at the same meridian, or same speed value, since the object moved at a constant speed, so the measured speed was the same at every value of time. This means that the tendency line volition be a horizontal line through the points.

This fact nigh horizontal tendency lines holds more generally. Whatever object that moves at a abiding speed for the entire fourth dimension its speed is measured will have the aforementioned value of speed at all measured values of fourth dimension. This ways that all of the points on a speed–time graph of the object will have the same height on the speed centrality, and so the trend line for the points will be a horizontal line.

Therefore, the motion of any object that moves at a constant speed can be represented on a speed–fourth dimension graph by a horizontal line. Nosotros tin can besides turn this argument on its head to say that whatsoever horizontal line on a speed–time graph must represent the move of an object that moves at a constant speed.

From left to right along the horizontal axis, or fourth dimension axis, the fourth dimension is increasing. The further right a bespeak is on the graph, the greater the value of time. Similarly, from bottom to meridian on the vertical axis, or speed axis, the speed is increasing. The higher up a signal is on the graph, the greater the value of speed.

When we take a horizontal line, representing motion at a constant speed, the college up that line is on the graph, the greater the speed of the object.

Suppose we have the following speed–time graph, which shows the motion of two objects that each move at a constant speed.

The graph shows two horizontal lines, each respective to a unlike object. Even without any numbers on the axes, nosotros may merely await at this graph and see that the blue line corresponds to an object moving with a greater speed. This is because the blueish line is college upward on the graph than the cherry-red line.

Let'due south look at an example problem.

Example ii: Working Out Which Line on a Speed–Time Graph Corresponds to the Greatest Constant Speed

Which color line shows the object that has the greatest speed?

1. Orange
2. Blue
3. Red

Answer

The graph shown in the question plots speed on the -axis confronting time on the -centrality, which means that it is a speed–time graph.

The graph shows three horizontal lines, each representing the motion of a different object. Since the lines are all horizontal, this means that nosotros know that each of the iii objects moves at a abiding speed.

We are asked to identify which line shows the object with the greatest speed.

We tin recall that the higher upwards a line is on a speed–time graph, the further information technology is along the speed axis. This means that the higher up a line is, the greater the speed that it represents.

In this diagram, the orange line is lowest. Therefore, this line corresponds to the slowest moving object.

The bluish line is higher than the orangish line, and then the object represented past the blue line moves with a greater speed than the object represented by the orange line.

The red line is the highest line of the iii. This means that the object represented by the cherry line moves with a greater speed than either of the other 2 objects.

Therefore, our reply to the question is that the object that has the greatest speed is shown by the cerise line. This is the answer given in option C.

The graph in this concluding example had no units or scale on either the time axis or the speed axis. This meant that we were not able to read off actual values of fourth dimension or the speed of the objects. All that nosotros could practice was identify whether i object was faster than another.

Nosotros have already seen how we may have specific values of time and speed and plot them on a speed–fourth dimension graph. In order to know where to plot the points, we needed a scale on both the time axis and the speed axis.

In the same way, if we take a speed–time graph with numbered scales on the axes, nosotros may use these to read off values of time and speed for plotted points or a line on the graph.

Consider the following speed–time graph, showing just a single plotted bespeak.

This point has 2 values associated with it: a time value, given past its position on the time axis, and a speed value, given by its position on the speed axis. The fourth dimension value is the time at which that measurement was taken. The speed value is the value of speed that was measured at that time.

To read off the fourth dimension value of the point, we trace straight vertically down from the indicate until we accomplish the fourth dimension centrality, as shown below.

The time value is the value on the time centrality at the position where our vertical line meets it. In this instance, that value is 4 seconds, which means that this particular measurement was taken at a time of iv seconds.

To read off the speed value of the bespeak, we trace directly horizontally across from the indicate until we reach the speed axis, as shown below.

The speed value is the value on the speed–time axis at the position where our horizontal line meets information technology. In this case, that value is two metres per second, which means that the speed of the object when this measurement was made was found to exist 2 metres per second.

If nosotros have a speed–time graph showing movement at a constant speed, we know that this volition be represented past a horizontal line. For example, consider the graph below.

We may pick any point on this line and trace down vertically to the time axis to find the time value associated with a particular position along this line.

Similarly, we may choose whatsoever point on the line and trace across horizontally to the speed centrality to notice the speed of the object at that instant. Since the motion is at a constant speed, and hence the graph shows a horizontal line, whatsoever point on the line we choose will trace beyond to the same value on the speed axis. Physically, this simply ways that the object has the same value of speed for all values of fourth dimension.

If we are trying to detect the speed of an object from a graph similar this in which the plotted speed is a horizontal line, the human action of tracing across from a detail point is unnecessary. All points on the line trace beyond to the same speed value—this is the value on the speed axis at the point where the horizontal line meets, or intersects, information technology.

Looking again at our item graph, nosotros can identify the value on the speed axis at the point where the horizontal line meets the axis.

The position at which the horizontal line meets the speed axis is indicated by a ruddy arrow on the graph. Nosotros can see that this position is at a value of 4 one thousand/s. Therefore, we now know that our object moves at a constant speed of 4 thou/s.

Let's have a await at another case question.

Case 3: Reading the Value of a Abiding Speed from a Speed–Time Graph

What is the speed shown by the speed–time graph?

Answer

This question shows us a speed–time graph and asks usa what speed is shown by the graph.

We can see that the graph shows a horizontal line. We may recall that this corresponds to motion at a constant speed.

To read off the value of the speed, we demand to place the pinnacle of this line on the speed axis, that is, the position on the speed axis at which the line meets, or intersects, this axis.

We can identify this position as shown in the diagram below.

The blue pointer points to the position at which the horizontal line meets the speed centrality. We tin can see that this is at a value of 3 m/s, and we know that this value must be the speed shown past the graph.

Therefore, our answer to the question is that the speed shown past the graph is 3 m/s.

Sometimes, we might have information about an object's motion given to us in the form of a altitude–time graph. We can think that a distance–time graph plots distance on the -axis against fourth dimension on the -axis.

In this case, nosotros can apply the information given to usa in the distance–time graph in order to work out how the speed–time graph for the object will await. We will see how to do this for a couple of simple cases.

We have seen that a horizontal line on a speed–time graph represents move at a constant speed. In other words, the speed of the object is non changing as fourth dimension goes on. So, what does a horizontal line on a distance–fourth dimension graph hateful?

Past the same logic, a horizontal line on a distance time graph must represent an object with a distance value that is not changing in time.

We can recall that speed is defined as distance moved per unit time. This means that if we have an object with a distance value that does non change during the time that we measure it, then that object has a speed of 0 m/due south; it is not moving.

Consider the following altitude time graph.

All three of the lines on this graph are horizontal. Therefore, all iii lines stand for objects that are not moving during the catamenia that the measurements used to plot this graph were taken.

Nosotros can notice that the lines are at different heights on the graph, corresponding to different values of distance. Perhaps the objects moved different distances earlier the first fourth dimension of the measurements taken for the graph. For our purposes, it does not matter what the value of altitude is; in all three cases, the distance does non change during the measurement period. This ways that all iii objects accept a speed of 0 m/s during this time.

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 speed–time graph shows a value of 0 1000/southward for every value of time. Therefore, it corresponds to an object with a constant speed of 0 m/s, in other words, an object that is not moving.

At present let's consider the following distance–time graph.

This graph shows an object whose distance increases at a constant charge per unit. We can see this as follows.

In the diagram beneath, we accept the same graph, but now we have highlighted 2 triangles. The hypotenuse of both triangles lies along the line plotted on the distance–fourth dimension graph.

The horizontal and vertical sides of the ruddy-dashed triangle each have a side length of 1. For the horizontal side, this is in units of seconds, while for the vertical side, information technology is in units of metres. What this triangle is telling u.s.a. is that the object travels a distance of ane m the first 1 s shown on the graph.

At present looking at the blue triangle, we see that the vertical and horizontal sides each accept a side length of 2. This tells u.s.a. that the object travels a full altitude of 2 m in the kickoff two s.

The sides of the blue triangle are in the aforementioned proportion every bit the sides of the red triangle. In fact, no matter where nosotros draw a triangle, so long as its hypotenuse lies along the line on the graph, we volition 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 remember that if an object moves equal distances in equal times, and so 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 volition be in the aforementioned proportion for whatever distance–time graph where the altitude increases with time as a directly line.

In other words, all distance–time graphs that bear witness a straight line represent move at a constant speed. Therefore, the corresponding speed–fourth dimension graph will always exist a horizontal line.

The steeper a line is on a distance–time graph, the greater the distance moved past the object in each unit of time. Nosotros can too call up that the greater the distance moved per unit fourth dimension, the greater the speed of an object. Therefore, we tin can see that the steeper the line on a distance–time graph is, the to a higher place the corresponding horizontal line will be on a speed–fourth dimension graph.

For example, allow's consider the diagram beneath.

Each color line on the distance–time graph corresponds to the same color line on the speed–time graph. On the distance–fourth dimension graph, the red line is the least steep. Therefore, this line shows the smallest speed. The smallest speed is represented by the everyman 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 ii.

Let'south expect at one more than example problem.

Example 4: Identifying Which Line on a Speed–Time Graph Corresponds to a Given Line on a Distance–Fourth dimension Graph

Which colour line on the speed–time graph shows the movement of the object on the distance–time graph?

Respond

In this question, we are presented with a altitude–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 altitude–fourth dimension graph.

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

Therefore, nosotros know that the distance–time graph shows the motion of an object that moves at a abiding speed.

If we at present look at the speed–time graph, we have two potential choices. Nosotros need to piece of work out whether it is the green line or the red line that represents movement at a constant speed.

The red line shows speed increasing as time increases. Since the speed is increasing, information technology cannot be abiding. So the red line cannot stand for the motion at a constant speed shown in the distance–fourth dimension 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 non changing; or, in other words, this green line shows motion at a constant speed.

And then, our reply to the question is that information technology is the greenish line on the speed–time graph that shows the move of the object on the distance–fourth dimension graph.

Let us now finish by summarizing what has been learned in this explainer.

Key Points

• We can show the motility of an object using a speed–time graph. This is a graph that plots speed on the -axis against time on the -centrality.
• Move at a constant speed is represented by a horizontal line on a speed–time graph. A line that is higher up on the graph represents a greater speed.
• If our speed–time graph has a numerical scale on the axes, we tin can read off the speed for a point plotted on the graph past tracing a horizontal line beyond from that point to the speed axis. The value on the speed axis where this line meets it is the speed at this point.
• Consider a horizontal line on a speed–fourth dimension graph, for an object moving at a constant speed. The line will run across, or intersect, the speed axis at some height. Reading the value on the speed centrality at this height gives u.s. the speed of the object.

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Source: https://www.nagwa.com/en/explainers/124101048651/

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