Need Help?

Get in touch with us


Graphs of Motion- Types of Motion Graphs

Grade 11
Aug 22, 2022

Graphs of Motion 


Introduction to the graphs: 

Generally, graphs are plotted between two variables, one is the independent variable, and another is the dependent variable 

Let’s say x is an independent variable and y is the dependent variable. If a graph is plotted between x and y (x,y), the following points should be remembered before plotting a graph. 

Points to be remembered: 

  1. An equation between C 
  1. If the graph is passing through the origin, then x=0 and also y=0. Suppose no graph is passing through the origin. 
  1. Differentiating y with respect to x can give the slope of the graph at that point. 
  1. To find out the area covered in the graph, integrate y along the x-axis. 
  1. Most asked graphs in motion are (s-t,v-t,a-t and v-s). 
Fig. No.1 

Graphs of uniform motion: 

The equations which appear in uniform motion graphs are  

a=0,v = const, s=vt or s=s0 + vt 

Fig. No.2

 Important points to remember: 

  1. St graph is linear, hence it is a straight line. 
  1. As v is constant, then the slope of the curve is constant. 
  1. As a=0, then the slope of the curve is zero. 
  1. S=vt graph starts from the origin.  
  1. s=s0 + vt graph may or may not start from the origin as displacement can be taken from any point on the graph. 

Graphs of uniformly accelerated motion: 

Generally, we encounter following equations in graphs of uniformly accelerated motion: 


a = 0(positive) 

v=u+at or v=at 

s=ut+1/2at2 or s=1/2at2 

s=s0+ut+1/2at2  or s=s0+1/2at2 

Fig. No.3

Important points to remember: 

  1. v-t is a straight line as it is linear in the graph. 
  1. s-t is a parabola as all the s-t equations are quadratic in the graph. 
  1. The slope of the s-t graph gives instantaneous velocity. As instantaneous velocity is positive and constantly increasing, the graph s-t is also positive and constantly increasing. 
  1. The slope of the v-t graph gives instantaneous acceleration, which is positive and increasing.  

Graphs of uniformly retarded motion: 

We encounter following equations using graphs of uniformly retarded motion 





Fig. No.4

Important motion: 

  1. The v-t graph cannot pass through the origin, hence u≠0, the slope of the s-t graph is not zero. 
  1. Velocity keeps decreasing from positive to zero. 
  1. The slope of the v-t graph gives instantaneous acceleration, which is negative and decreasing. 
  1. The slope of the s-t graph gives instantaneous velocity. As instantaneous velocity is positive and constantly decreasing, the graph s-t is also positive and constantly decreasing. 

Graphs of uniformly retarded motion and then accelerated motion: 

In this case, the graphs are drawn, and the following points are noted for the use of graph 

Let us consider a ball is thrown vertically upwards 

Fig. No.5 

Important points: 

  1. If a =-9.8, then the motion is under gravitational force  
  1. In the graphs, O is the origin. 
    v=u and slope tanϴ=u 
  1. In (graph 3) A is the maximum height of the ball reached 
    v=0 and the slope tanϴ=0 
  1. B in (graph 3) is returning the ball to the ground 
    v=-u and the slope tanϴ=-u 


Related topics

Types of Waves

Different Types of Waves and Their Examples

Introduction: We can’t directly observe many waves like light waves and sound waves. The mechanical waves on a rope, waves on the surface of the water, and a slinky are visible to us. So, these mechanical waves can serve as a model to understand the wave phenomenon. Explanation: Types of Waves: Fig:1 Types of waves […]

Dispersion of Light

Dispersion of Light and the Formation of Rainbow

Introduction: Visible Light: Visible light from the Sun comes to Earth as white light traveling through space in the form of waves. Visible light contains a mixture of wavelengths that the human eye can detect. Visible light has wavelengths between 0.7 and 0.4 millionths of a meter. The different colors you see are electromagnetic waves […]


Force: Balanced and Unbalanced Forces

Introduction: In a tug of war, the one applying more force wins the game. In this session, we will calculate this force that makes one team win and one team lose. We will learn about it in terms of balanced force and unbalanced force. Explanation: Force Force is an external effort that may move a […]


Magnets: Uses, Materials, and Their Interactions

Introduction: Nowadays magnets are widely used for many applications. In this session, we will discuss the basics of magnets and their properties, and the way they were and are used. Explanation: Magnets: Magnetic and Non-magnetic Materials: Poles of a Magnet: Fig No. 1.2: Poles of a magnet Compass: Interaction Between Magnets: The north pole of […]


Other topics