Skip to content 
Verification of three equations of motion
Verifications of Newton’s three equations of motions
Three equations of motions -These three equations of motions were discovered by the great British scientist so these three equations of motions are also called Newton’s three equations of motions. In this post, you will study the verifications of Newton’s three equations of motions by the graphical method and algebraic method. Before we study three equations of motion lets make a flashback, the relationship between distance and time is that distance is the product of speed and time, you already have studied in junior classes.
NCERT Solutions Class 10 Science from chapter 1 to 16
When the direction of moving object is taken under consideration then the distance is substituted by displacement, speed by velocity and since time is the scalar quantity it remains the same. Displacement is the product of velocity and time. This formula has its limitation if the speed of the object varies with time. If a bus moves in the way with variable speed and reached to a destination within a certain time period. Then how will you calculate the total distance traveled? Yes, here we are needed to apply one or a couple of the three equations of motions to calculate the total distance. This formula, distance = speed × time is applied only when speed is constant. In class 9, before you study three equations of motions you have to study now one more physical quantity i.e acceleration.
You can also study related topics
Three Laws of Motion: Class 9 CBSE
Average Speed and Average Velocity: Differences
How to evaluate recoil velocity of gun
If energy is conserved then why do we need to save it for future generations?
What is second law of of motion ?
What is universal law of gravitational force
Acceleration. Acceleration is the rate of change of velocity, in simple words, the velocity of speed is the acceleration or the rate at which the velocity varies.
Let u is the initial velocity of an object and in time t its velocity become v
Then the change in its velocity = v – u
Where ‘a’ is the acceleration of the object.
Three equations of motion can be verified by three methods, here are given two methods, Algraibic and graphical, the third way is by calculus, you will study in class 11.
Verifications of Newton’s three equations of motions
The first equation of motion.
Algebraical method of verification of the first equation of motion.
It is derived from the definition of the acceleration
v = u + at⇒First equation of the motion
Verification of the first equation of motion by graphical method.
Velocity and time graph of an object is drawn as following in which velocity is shown on y-axis and time is shown on the x-axis
Graphically, the acceleration is shown by the slope of the graph
DE = OA = u, BE = v and AD = OE =t
The second equation of motion
Verification of the second equation of motion by the algebraical method.
Displacement (s)= average velocity ×time taken
Average velocity = (v + u)/2 and time = t
The verification of the second equation of motion by graphical method.
If the velocity is constant, then the displacement covered is given by DE × OE= area of rectangle AOED
Therefore the total displacement covered by the object in the velocity-time graph can be shown by sum of the area of rectangle and triangle.
Displacement = Area of rectangle AOED + Area of triangle ABD
AD = OE =t, OA = DE = u, BD = BE – DE = v – u
From (i)
v –u = at
The second equation of motion
Purchase world class latest computers and accessories
Third equation of motion.
Verification of the third equation of motion by the algebraic method
The displacement = average velocity × time period
average velocity = (v + u)/2, time = t
From (i), t = (v – u)/a
v² – u² = 2as
Verification of the third equation of motion by the graphical method.
Displacement = Area of trapezium ABEO
AO = u, BE =v, OE = t
From (i) substituting t = (v – u)/a
v² – u² = 2as
⇒Third equation of motion
You can see video
Verification,of three equation of Motions by the method of calculus
First equation of motion: Let an object ‘s initil velocity is u and within time t ,it achieves velocity v
The rate of change of velocity(v) is acceleratiom(a)
dv = a dt
Integrating both sides
∫dv = ∫a.dt
This is the case when acceleration is uniform(constant) and initial velocity is u and final velocity is v
v – u = a[t-0]
v-u = at
v-u = at, is the first equation of motion
Verification of three equation of motion by the method of calculus:
Verification of first equation of motion by the method of calculus:
We know the acceleration = Rate of change of velocity
Let there occures a small change (dv) in velocity within small time span of dt,then acceleration a, can be written as follows
Integrating LHS with respect to time within the limits of time from 0 to t and Integrating RHS with respect to velocity within the limits of velocity from u to v
Since acceleration is constant here
a(t -0) = (v – u)
at = v – u
First equation of motion v -u= at is verified
Verification of second equation of motion by the method of calculus:
We know displacement is the minimum distance travelled by an object in unit time
Let a small distance ds is travelled by an object within a small time span dt
Integrating LHS with respect to displacement within the limits of displacement from 0 to s and Integrating RHS with respect to time within the limits of time from 0 to t
u and a supposed as a constant value
Here it is the verified third equation of motion
Verification of third equation of motion by the method of calculus:
For driving third equation,we are needed to define acceleration and velocity
From (i) and (ii) equation, we get
Integrating LHS with respect to displacement within the limits of displacement from 0 to s and Integrating RHS with respect to velocity within the limits of time from u to v
v² – u² = 2as
Third equation of motion v² – u² = 2as is varified
Important Science Notes for Class 9 and 10 grade
Class 10 CBSE Science Notes
Human reproductive systems of Male & Family
Modes of reproduction used by single organisms-Asexual reproductions
The structure and anatomy of the Heart
Anatomy of the Human brain-Class 10 CBSE
NEET Sylabus and its preparation
Myopia, Hypermetropia and Presbyopia
Human eye structure and its function
Electrical resistance and conductance
Electric Current and Heating effect of Electric Current
What is a potential difference across an electric field ?
Why do the star twinkle but planets don’t
Light reflection, refraction, scattering, and dispersion
Class 10 chemistry Viva Voce Questions and Answers
Class 10 Physics Viva Voce Questions and Answers
Class 10 Chemistry Practical Based Questions and Answers
What are the physical and chemical properties of metals?
Type of Chemical Reactions with Complete detail
Chemical properties of Acids and Bases-A note for grade 10 students
What is pH value and its importance in everyday life.
Difference between soaps and detergents
Extraction of metals as per the activity series
Ionic and covalent compounds and the difference between them
Class 9 CBSE Science Notes
Three Laws of Motion: Class 9 CBSE
Evoporation,Vapourization and Latent heat -Class 9 CBSE notes
What is an atom,molecule and atomicity of a substance?
How to determine Valency,net charge of an ion and Molecular formula of a substance.
Thrust and Pressure : Difference
The Complete Detail of Archimedes Principal
Average Speed and Average Velocity: Differences
How to evaluate recoil velocity of gun
If energy is conserved then why do we need to save it for future generations?
Molar mass,molecular mass and mole concept
What is second law of of motion ?
What is universal law of gravitational force
NCERT Solutions of Science and Maths for Class 9,10,11 and 12
NCERT Solutions for class 9 maths
NCERT Solutions for class 9 science
CBSE Class 9-Question paper of science 2020 with solutions
CBSE Class 9-Sample paper of science
CBSE Class 9-Unsolved question paper of science 2019
NCERT Solutions for class 10 maths
CBSE Class 10-Question paper of maths 2021 with solutions
CBSE Class 10-Half yearly question paper of maths 2020 with solutions
CBSE Class 10 -Question paper of maths 2020 with solutions
CBSE Class 10-Question paper of maths 2019 with solutions
NCERT Solutions for Class 10 Science
Solutions of Class 10 Science Sample Paper and Question Papers for Term-1 and Term 2 2021-22 CBSE Board
Solution of Class 10 Science Question Paper Preboard 2021-22:Term 2 CBSE Board Exam
Solutions of Class 10 Science Sample Paper Term-1 2021-22 CBSE Board
Class 10 Science Sample Paper for Term 2 CBSE Board Exam 2021-22 with Solution
Solutions of Class 10 Science Question Paper Preboard Examination (First) 2021 -22 Class 10 Science
CBSE Class 10 – Question paper of science 2020 with solutions
CBSE class 10 -Sample paper of Science 2020
NCERT Solutions for class 11 maths
| Chapter 1-Sets | Chapter 9-Sequences and Series |
| Chapter 2- Relations and functions | Chapter 10- Straight Lines |
| Chapter 3- Trigonometry | Chapter 11-Conic Sections |
| Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |
| Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |
| Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |
| Chapter 7- Permutations and Combinations | Chapter 15- Statistics |
| Chapter 8- Binomial Theorem | Chapter 16- Probability |
CBSE Class 11-Question paper of maths 2015
CBSE Class 11 – Second unit test of maths 2021 with solutions
NCERT solutions for class 12 maths
| Chapter 1-Relations and Functions | Chapter 9-Differential Equations |
| Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |
| Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |
| Chapter 4-Determinants | Chapter 12-Linear Programming |
| Chapter 5- Continuity and Differentiability | Chapter 13-Probability |
| Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |
| Chapter 7- Integrals | |
| Chapter 8-Application of Integrals |
Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2
Class 12 Maths Important Questions-Application of Integrals
Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22
Solutions of class 12 maths question paper 2021 preboard exam CBSE Solution
