Position Time Graph To Velocity Time Graph: Exhaustive Insights And Facts

This post let us know the different aspects of the Position time graph to velocity time graph and their relation.

The relation between position time graph to velocity time graph is that the V-T graph is derived from the P-T graph. The primary difference between them is that the velocity-time graph tells about the body’s speed and position-time about the absolute path traveled by the particle in motion.

The transition from a Position-Time Graph (PTG) to a Velocity-Time Graph (VTG) is achieved through the process of differentiation. In simpler terms, the slope or gradient of the position-time graph at any given point gives the velocity at that point, which can then be plotted on the velocity-time graph.

Key Points :

Here’s a table that helps summarize the relationship:

Aspect	Position-Time Graph	Velocity-Time Graph
Y-Axis	Position (Displacement)	Velocity
Slope Represents	Velocity	Acceleration
Horizontal Line	Constant position (no movement)	Constant velocity
Upward Sloping Line	Positive velocity	Positive acceleration
Downward Sloping Line	Negative velocity	Negative acceleration
Steeper Slope	Greater velocity	Greater acceleration
Curve Upwards	Increasing velocity	Positive acceleration
Curve Downwards	Decreasing velocity	Negative acceleration
Area Under Curve	Not commonly used for interpretation	Displacement from a point in time
Intercept with Y-Axis	Initial position	Initial velocity

Some things to keep in mind:

The x-axis is time in both cases.
The transition from a position-time graph to a velocity-time graph involves finding the slope at each point on the position-time graph. This can be done by calculating the derivative in the context of calculus.
The velocity-time graph can then be used to determine acceleration by looking at its slope or the rate at which velocity changes.
Similarly, the transition from a velocity-time graph to an acceleration-time graph involves finding the slope of the velocity-time graph.

Now let us know about different insights of these two graphs as it is the post’s primary focus.

Position time graph to velocity time graph examples

The following graphs are some examples of position time to velocity-time graph transitions.

If we consider the race of rabbit and tortoise as an example, we can plot both the graphs as follows if we take the change in distance and velocity.

position time graph to a velocity time graph — Image: Position-time graph

Again, if we consider one more example of an athlete in a marathon, we can consider the change in his position and velocity and plot it below.

The slope on the P-T graph shows the velocity in both examples, and the area under the V-T graph accelerates the considered characters.

Now let us see into some examples of P-T graphs.

Position vs time graph examples

By looking at the examples of the position-time graph, we can understand them better.

Consider a person going on a walk at a specific rate. Then he feels to jog, there is a transition of position with time, and by plotting the values, the P-T graph obtained will be as below it represents an increase in velocity.

Consider a truck that moves on a linear path without taking any turn; if we plot the P-T graph for its value, we obtain a linear graph representing the constant velocity.

These are some examples of P-T graphs.

Position vs time graph

The P-T graph generally indicates the velocity/speed of the body in motion.

A position vs. time graph indicates the distance of path that the particle has traveled, considering from its beginning point to the final point of the movement. It has a time interval on its x-axis and position on the y axis. If the slope is steep, it indicates that it has a large slope, and the particle speed changes quickly.

Now let us know how to convert a P-T graph to a velocity-time graph.

How do you convert a position time graph to a velocity time graph

To convert a position-time graph to a velocity-time graph, we have to follow some simple steps;

We know that the derivative of the P-T graph is the Velocity time graph. You can also measure it by using the formula.
If we calculate the slope of the P-T graph, then we obtain velocity as a result.
After obtaining the velocity, we can plot the V – T graph under it and calculate the area under it to measure acceleration.

In this way, we can convert position time to the velocity-time graph.

Is position time graph same as velocity time graph

Both the graphs are different from each other in finding some aspects.

The main difference between the P-T graph and the V-T graph indicates the body’s speed depending on the increase or decrease in the vehicle. At the same time, the P-T graph indicates the movement of that body over a certain period.

Now it’s time to study the relationship between the P-T graph and velocity.

How does position and time relate to velocity

To measure the velocity of a particle, the concept quantities position and time are required.

Should know the position and time of the object to calculate the velocity of the particle that is traveling. If any of the quantities are not known, then it won’t be easy to measure the velocity of that particle. They are related to each other by formula and even by the slope of the P-T graph that calculates velocity.

Now let us know how position affects the velocity of a body.

How does position affect the value of velocity

The slope of the P-T graph directly affects knowing the nature of velocity.

We know that by looking at the value of slope on the P-T graph, we can find the nature of velocity, i.e., we can say that,
The constant value of a slope on the P-T graph indicates the object has constant velocity.
Changing slope indicated variable velocity.
If the slope is downwards or from left to right, it will be considered negative velocity.

The direction of the slope of the P-T graph represents the nature of velocity.

Importance of Velocity-time graph

To know the measure of acceleration and displacement V-T graph is useful.

We know that we can calculate two different quantities from the two different elements of the V-T graph, i.e., by knowing the value of the slope of the V-T graph, we can find its acceleration. In the same way, by calculating the area under its curve, we can measure the object’s displacement.

Now let us know the importance of the P-T graph.

Importance of position-time graph

In the P-T graph, we can calculate the distance traveled by the body in its motion and taken time.

We can measure the body’s motion at a specific time interval on a position-time graph. After plotting the values on the x and y-axis and joining the values, we can measure the slope, and this slope signifies the value of the velocity of that body.

Both the graphs have their importance.

Frequently Asked Questions | FAQs

How does constant velocity look like on a position-time graph?

To know about how the graph of constant velocity looks on a position-time graph, we can see below,

If we plot a graph of position with time and the body in the motion traveling with constant velocity, the graph will be in the form of a straight line. We sometimes observe the horizontal line on a position-time graph, which symbolizes zero velocity.

Can distance-time graph and velocity-time graph be similar?

Two different quantities can be found on the position-time graph and velocity-time graph.

The position-time graph involves the object’s position change, and the time represents the amount of distance moved by that object in a particular period. At the same time, the slope or area under the velocity-time graph line indicates the object’s acceleration within a particular time.

What is the method to find out the V-T graph?

As the name indicates, we can use a graphical method to find the velocity value.

First, choose any two points on the curve and find their coordinates.
Take the difference of the two chosen points along both the y and x-axis.
In the third step, divide the values of the y-axis with the values of the x-axis.
The obtained value is turned out to be the value of the required quantity.

What do position-time graphs show?

The P-T graph represents the amount of change in the position of a body in motion.

In general terms, we can tell that a position-time graph can represent the amount of distance or the change in position of a body, taking into consideration from the beginning to end of the particular motion in a simple manner.

How do you describe a position-time graph?

We can take the help of slope on a P-T graph to describe it.

In a P-T graph, the change in velocity of a body is obtained by calculating the slope/steepness of the line on the graph. If the graph is linear or flat, then the body’s position is constant. If the line is steeper, there will b an increase in a curve, and the body moves faster.

Can we create an accurate position vs. time graph using a velocity vs. time graph?

Cannot create the accurate position vs. time graph from the velocity vs. time graph.

We know that a P-T graph gives the total amount of distance traveled by the body. But on a V-T graph, the slope signifies the value of change in velocity and gives no information about the position of that body. From this, we can say that it is impossible to create an accurate P-T graph from a V-T graph.

What kind of graph do we obtain if we plot the position-time graph of the moving truck?

Here are some consequences are given below that might help know the nature of the graph.

The kind of graph will usually depend on the nature of motion.
The P-T graph will not be linear to the x-axis since the time does not remain the same.
Similarly, the P-T graph will not be linear to the y-axis since it is not stationary does not remain the same.
It will not be a parabola curve, as time cannot be negative.
Finally, we can tell that it will have some measurable slope and a line to obtain the velocity value.

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Raghavi Acharya

I am Raghavi Acharya, I have completed my post-graduation in physics with a specialization in the field of condensed matter physics. I have always considered Physics to be a captivating area of study and I enjoy exploring the various fields of this subject. In my free time, I engage myself in digital art. My articles are aimed towards delivering the concepts of physics in a very simplified manner to the readers.