Distance Time Graph and Velocity Time Graph - Definition, Examples, FAQs

Introduction:
In this article we will discuss about distance time graph for uniform motion and velocity time graph for uniform motion. We will cover the topics like what are the uses of distance time graph and uses of velocity time graph and how uniform motion graph and uniform velocity graph will differ. We will study in detail about the graphical representation of motion.

Distance – Time graph

What is Distance time graph?

Distance - time graph represents the distance covered by an object from the starting point against the time. In the graph, time is taken alongside X - axis and distance is taken alongside Y- axis.

Uses of distance time graph:

• The graph of distance and time is used to determine the position of an object at any time in the given time interval.
• To determine the speed of an object at any time in the given time interval.

The graph of uniform and non - uniform motion of an object can be studied on the basis of distance - time graph. Let us now draw distance time graph for uniform and non uniform motion to understand it clearly.

Point to be noted: area under distance time graph is nonentity

Equation of distance time graph=

Slope = speed = distance/time

Also read -

• NCERT Solutions for Class 11 Physics
• NCERT Solutions for Class 12 Physics
• NCERT Solutions for All Subjects

For uniform motion:

Let us study the position time graph for uniform motion along the straight line. We know, when an object covers the same distances in the same intervals of time it is said to be in uniform motion.

Let’s take an example of distance time graph for uniform motion class 9, a school bus moving is moving in a straight line and covers following distances in given time interval.

Fig. (i)

In Fig. (i) First column shows time in unit "seconds" and second column shows distance in unit "meters ". Now let us draw distance time graph for uniform motion taking time along X - axis and distance along Y - axis.

X-axis scale of the graph is:

1centimeter = 10 seconds

Y-axis scale of the graph is:

1 centimetres = 15 meters

Fig. (ii)

What does distance time graph represent?

As the distance time graph of uniform motion is a straight line, distance and time are directly proportional to each other that means an object covers equal distance in equal intervals of time in case of uniform motion. Slope of the straight line in distance time graph of an object moving with uniform speed gives the speed of the moving object.

For non – uniform motion:

Let us study the distance time graph for non uniform motion along the straight line. We know, when an object covers uneven distances in equivalent intervals of time it is said to be in uniform motion.

Let’s take an example from distance time graph class 9, a car is travelling in a straight line in a non – uniform motion with the following distances in given time interval.

Fig. (iii)

In Fig. (iii) first column shows time in unit "seconds" and second column shows distance in unit "meters ".Now let us draw position time graph taking time along X - axis and distance along Y - axis.

Fig. (iv)

X-axis scale of the graph is:

1centimeter = 5 seconds

Y-axis scale of the graph is:

1 centimetres = 5 meters

What does distance time graph represent?

As the distance and time graph is not a straight line, we can say that distance is not proportional to time. In other words, in case of distance time graph for non uniform speed distance does not change uniformly with time.

Distance time graph for a body at rest:

In distance time graph for body at rest, the graph will show a line parallel to x axis.

The parallel line shows that the time is changing but the position of the body is same.

Let us now draw a distance time graph for an object at rest.

Fig. (v)

Velocity – time graph

What is velocity – time graph according to distance time graph for class 9?

The velocity time graph is a graph in which the Velocity varies with the time for an object moving in a straight line. In this graph, time is taken alongside X - axis and Velocity is taken alongside Y- axis.

Uses of v vs t graph:

• To determine the magnitude of the displacement (distance).
• To get the information about the acceleration of an object.

Answer to the question how to calculate distance from velocity time graph/ how to find distance from velocity time graph: The area enclosed by the Velocity time graph gives the magnitude of displacement. The uniform and non - uniform motion of an object can be studied on the basis of Velocity time graph for class 9.

Velocity time relation =

Slope = acceleration = velocity/time

For uniform velocity:

Let us study the Velocity time graph examples for understanding uniform motion along the straight line. We know, when an object covers the same distances in the same interims of time it is said to be uniform motion.

Let’s say we have an information about a moving car having velocity in unit “meter per seconds” and time in unit “seconds”. In this graph time is taken alongside X - axis and Velocity is taken alongside Y- axis.

Fig. (v)

Now let us draw Velocity time graph for uniform motion in order to understand it further.

Following is the Velocity time graph for uniform velocity.

X-axis scale of the graph is:

1centimeter = 10 seconds

Y-axis scale of the graph is:

1 centimetres = 10 meter per seconds.

Fig. (vi)

If the object moves in uniform motion, then, the Velocity vs time graph will show a line parallel to the x - axis (i.e. time interval).

What can we understand from this graph?

This is a constant velocity graph. We know that acceleration is defined as rate of change of velocity but here we do not have any change in the velocity throughout so we can say there is no acceleration. So it is a zero acceleration graph.

So whenever we notice a velocity-time graph parallel to x-axis we can conclude two things-first, the body is moving with uniform velocity and second ,the acceleration is zero.

NCERT Physics Notes :

• NCERT Notes class 11 physics
• NCERT Notes class 12 physics
• NCERT Notes for all subject

For uniform accelerated motion (increasing):

Let us study the velocity time graph for uniform acceleration motion,

Let’s say we have an information about a moving car having velocity in unit “meter per seconds” and time in unit “seconds”. In this graph time is taken alongside X - axis and Velocity is taken alongside Y- axis.

Fig. (vii)

Now let us plot the vt graph for uniform motion in order to understand it further.

Following is a velocity time graph of uniform motion.

Fig. (viii)

X-axis scale of the graph is:

1centimeter = 10 seconds

Y-axis scale of the graph is:

1 centimetres = 5 meter per seconds.

What does velocity time graph represent?

We get a increasing graph or we can say again we get a straight line but this time it is not parallel to x-axis. It is inclined to x-axis. In velocity time graph of uniform acceleration, we can see the velocity is increasing uniformly with time and we get a positive acceleration graph.

The graph for uniform acceleration or uniform acceleration graph or uniform motion graphs or uniformly accelerated motion graph conclude that the body is moving with uniformly increasing velocity and the acceleration of a particle is increasing linearly. A particle starts from rest its acceleration versus time graph gives the maximum velocity of the particle.

A force time graph for the motion of a body gives the change in linear momentum of the body.

For uniform accelerated motion (decreasing):

Let us study the velocity time graph for uniformly accelerated motion,

Let’s say we have an information about a moving car having velocity in unit “meter per seconds” and time in unit “seconds”. Let’s draw velocity time graph for a car moving with uniform acceleration. In this graph time is taken alongside X - axis and Velocity is taken alongside Y- axis.

Fig. (ix)

What does velocity time graph represent?

Now let us try to infer what this graph is telling us. This velocity-time graph is again a straight line but it has a negative slope. This type of velocity-time graph means that there is a body which is having uniformly decreasing velocity. Hence we have the negative (constant) acceleration or the acceleration is retarding.

Also read :

• NCERT notes Class 11 Physics Chapter 3 Motion in a straight line
• NCERT solutions for Class 11 Physics Chapter 3 Motion in a straight line
• NCERT Exemplar Class 11 Physics Solutions Chapter 3 Motion in a straight line

For non - uniform accelerated motion:

Let us study the velocity time graph for non uniform motion.

Say we have information about a moving car having velocity in unit “meter per seconds” and time in unit “seconds”. Let’s draw a velocity time graph for non uniform acceleration. In this graph time is taken alongside X - axis and Velocity is taken alongside Y- axis.

Fig. (x)

What can we understand from this graph?

The velocity time graph for non uniform acceleration shows irregular figures, it is all mixed up. In this case we can say the body is moving with non - uniform velocity. Hence the acceleration in the vt graph is not constant, it is variable.

Also check-

• NCERT Exemplar Class 11th Physics Solutions
• NCERT Exemplar Class 12th Physics Solutions
• NCERT Exemplar Solutions for All Subjects