Slope Of Position Time Graph: Exhaustive Insights And FACTS


The graph is the representation of any two physical quantities with respect to each other. This article is about the slope of position time graph

A position-time graph of an object represents position and time on the two respective axes. It infers how far an object moves in a given time. The slope of position and time graph represents the velocity of the subject. From the points on the slope, we can find the velocity at a given time. 

The steepness of the slope tells about the direction of the given quantity. Just by looking at the slope, you can know a lot about the given graph. To calculate the slope of the graph, take two points on the line. Draw the vertical line from one point that is known as rising, and a horizontal line from another called to rise. The slope thus is the ratio between the rise and run, that is:

slope=rise/run

Slope of the graph
Positive and Negative Slope

From moving from left to right, if the slope runs upward, as shown in figure (i), then it is taken as positive. If the slope runs downward, as shown in figure (ii), then it is taken to be negative. 

What is the slope of position time graph

For the position and time graph, we take one quantity on the x-axis and the other one on the y-axis. It determines the motion of the object, i.e. from the graph, we get to know about its position at any particular time. The steepness, length and shape of the graph determine how an object is moving. 

The slope of position time graph is found by plotting the graph, and then on joining the points, we get a line either rising up or down. This line is the slope of the graph. By following the steps described above, we can determine the value of the slope. 

What does the slope position-time graph signify

The slope of the position-time graph reveals the magnitude of the velocity of a moving particle. It tells vital information about the velocity of a particular object. For instance, a small slope signifies a smaller velocity; a negative one leads to a negative value of velocity. 

At the same time, a constant slope determines the constant velocity, and if the slope keeps changing, that is, a curved line leads to a changing velocity. Therefore the slope of a position-time graph can be positive, negative, constant or changing by making a curved line. The value can also be zero in case the slope line is parallel to the time axis. 

Slope of position time graph

Suppose we are given the position-time graph as above, now; to determine the slope of the graph, we take two points as A and B on the line. From these two points, we draw perpendicular lines. The next step is to calculate the slope as:

slope=rise/run

Therefore the velocity of the object in that particular time would be 2 m/s. 

For the above graph, how will we find the position of the body when time equals 5 seconds. We can see that when the time t = 5 seconds, the position axis is marked at 2 m. Therefore the position of the object is 2 meters in 5 seconds. 

What is slope of a position vs time graph called

The slope of the position vs time graph is called velocity; it is also termed as displacement per unit time. The slope of this graph is determined as:

dx/dt=Displacement/time

We know the displacement/ time gives us the value of velocity. Therefore we have;

dx/dt=velocity

Hence its unit equals m/s. If the slope is steeper, it tells that the velocity is greater. 

If the position of the graph is increasing with time, then the slope is also positive velocity. Then the velocity increases or remains constant. If the velocity increases, then the body is accelerating.

 If the position is decreasing with time, the slope gives negative velocity. Which eventually means that body is decelerating. 

Slope of position time graph
Positive and Negative Slope of Position Time Graph

In the above figure, the first figure (i) shows the positive velocity and upward slope. At the same time, the second slope (ii) with a downward slope determines the negative velocity. 

Variations in the slope

In the above figure from O to A, the slope is positive, then from A to B it is zero and at last from B to C, the slope is negative. 

What is the use of position-time graph

The slope of position time graph is used to find the velocity of the given object. It is simpler to find the average velocity using the graph. The graph depicts the motion of any given body.

By plotting the graph, we can find the position at the given time and time at the given position. Graphical representation is an effective way of finding detailed information about the motion of a body in a small and efficient way. 

Motion of 3 Persons

In the above graph, the position-time of 3 persons A, B and C are plotted. It is clearly visible that the slope of B is the greatest; hence its velocity is the highest. Secondly, we can see that the line of all the three persons intersects at point P, which means that they will be at that same position in the given time. 

Therefore, the slope of position time graph is very useful to know all about the motion of two or more objects with respect to each other. It tells about the distance of the object at a particular time.  

What does the intercept of a position-time graph represent

The points where the graph intersects the x-axis and y-axis are known as intercepts.

The position-time graph has two axes and thus two intercepts. One is an x-intercept, and the other one is a y-intercept. Where the line of slope strikes the x-axis (horizontal) is called an x-intercept, whereas the y-intercept is defined as the point where the graph intersects the y-axis (vertical).

If we take the position on the y-axis, then the y-intercept tells about the starting position of the moving object. At that instant, time would be zero. 

To understand this, take a look at the graph above. Two cars start at the same time. Car A has its initial position as 0, but car B has its initial position of 1 cm as its line has a y-intercept at 1. 

Similarly, if we take the time on the x-axis, then the point where the graph will intersect will be the x-intercept of time. At this point, the position of the moving object would be zero. 

How does a position vs time graph look

In the position time graph, the x-axis denotes the time, and on the y-axis, the position is depicted. Look at the above figure; it is the position time graph. This is how the graph looks. Let’s try to plot a graph and understand it better. 

Table showing the motion of a car

The above table shows us the data of a moving car. The position of the car at different intervals of time is given. Now, let us take the time on the x-axis and position it on the y-axis. Now start plotting the points. 

Once you have plotted all the given coordinates, the last thing is to join them, and you will get the required position-time graph. 

Slope of position time graph of the object is at rest

We have talked about the slope being rising up, down and curved. Now for an object at rest, what would be the value of the slope, and how will it look?. Well, for the rest object, the slope is zero. 

The slope is parallel to x-axis

When the slope of the position-time graph is zero, it means that the body is not moving at all. Therefore we get the graph as the line parallel to the time axis that is the x-axis. It means that the object’s position will remain the same for the different time periods. 

Frequently Asked Question (FAQs)

What is a position-time graph? 

A graph is a mathematical and visual representation of any two or three physical quantities. 

Position-time time graph is the representation of the position and time of a moving object. It describes the motion of the body. The graphical representation is useful by telling us about the position of the moving body in a given time.  

What physical quantity do we calculate by the slope of the position time graph? 

By calculating the slope of the position and time graph, we get the value of velocity.

The slope of any moving body is calculated as:

Slope = change in vertical value/ change in horizontal value

Which gives the value of the velocityThe unit of velocity is m/s. 

Can the slope of the position-time graph be negative?

Yes, the slope of the position and time graph can be negative. 

It depicts the negative velocity of the body. When moving from left to right, if the slope moves downward, then the value of it would be negative, which is possible. The slope can be negative, positive, zero, or keep ls changing. 

Is slope always straight for the position-time graph?

The slope of the position and time graph does not always have to be straight. 

The straight slope depicts that either the velocity is increasing or decreasing. The slope can be curved; this tells that the velocity is continuously changing. The line of slope can be either be straight or curved. 

What information does the position-time graph provide?

With the position-time graph, you can know all about the motion of a particle.

By finding the slope of the position and time graph, we get to know all about the motion of the body. The negative slope indicates negative velocity. It also tells about the starting position of the object. 

How will we know that the object is not moving from the position-time graph? 

The slope can either be negative, positive or zero. 

The slope would be zero when the line of graphs is parallel to the time axis. This would mean that the position of the object remains the same for different times; that is, it is not moving.  

Rabiya Khalid

Hi,  I am Rabiya Khalid, currently pursuing my masters in Mathematics. Article writing is my passion and I have been professionally writing for more than a year now. Being a science student, I have a knack for reading and writing about science and everything related to it. If you like what I write you can connect with me on LinkedIn: https://www.linkedin.com/mwlite/in/rabiya-khalid-bba02921a In my free time, I let out my creative side on a canvas. You can check my paintings at: https://www.instagram.com/chronicles_studio/

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