Kinematics Revision Notes for JEE Main: Formulae & Key Concepts

The Kinematics chapter covers the fundamental branch of physics that is essential for understanding the motion of objects in different situations. This is a crucial chapter for JEE Main Exams, and you can expect at least 3 questions from it. Check out how many questions were asked from the Kinematics chapter in the last five years of JEE Main exams.

To reach your goals, prepare for your JEE Main 2025 exams using Vedantu’s Kinematics Notes PDF and the JEE Main Physics Syllabus 2025.

Kinematics JEE Main 2025: Important Topics

Here are a few Important topics students should pay attention to when learning the Kinematics chapter. These subjects are selected from previous years' JEE Main exams. Therefore, before you get the Revision notes, you can review this list of significant topics from Kinematics.

1. Motion along a Straight Line

• Kinematics is a branch of physics that deals with the study of the motion of a point body, the system of bodies without considering the cause of the motion.

• The motion is in which an object moves in a straight line and only one coordinate of the object changes with time.

• Motion along a straight line can be represented as motion along with an x-axis.

• Eg: The motion of a car along a straight line, a ball under free fall.

• Instantaneous velocity is the velocity of an object at a particular instant.

$v=\lim_{\Delta t \rightarrow 0} \dfrac{\Delta x}{\Delta t} = \dfrac {dx}{dt}$

• Instantaneous acceleration is the rate of change in velocity at a particular instant.

$a=\lim_{\Delta t \rightarrow 0} \dfrac{\Delta v}{\Delta t} = \dfrac {dv}{dt}$

2. Graphs for Different Types of Motion

For uniform motion, velocity remains constant. Velocity is not constant under non-uniform motion. For uniform velocity motion, acceleration remains constant.

• Displacement-time graph: The slope of a displacement time graph gives velocity.

• Velocity-time graph: The slope of a velocity-time graph gives the displacement covered by the body.

• Acceleration-time graph: The area under the curve of the acceleration time graph gives the change in velocity.

3. Motion under Gravity

• If a body is thrown vertically upward or released from a height, it moves in a straight line under the influence of gravity.

• A motion under gravity is a uniformly accelerated motion. Therefore, we can apply kinematics formulas.

• While applying kinematics formulas, each term has to be substituted with a proper sign.

• You can take an upward or downward direction as a positive sign. But remember that the opposite direction should be given a negative sign.

• In the diagram below, a ball comes down after it is thrown upward. If the upward direction is taken as +ve, then initial velocity is +ve(upward direction) and final velocity and acceleration are -ve due to gravity is -ve because their direction is in the downward direction.

4. Motion along a plane

• Motion along a plane is also called two-dimensional motion.

• For a body in two-dimensional motion,  its motion can be represented along with an XY plane.

• Examples: circular motion, projectile motion

5. Vector addition

• Parallelogram law of vector addition: If two vectors can be represented as two adjacent sides of a parallelogram, then the diagonal of the parallelogram represents the resultant vector of the two vectors.

6. Resolution of a vector into rectangular components

• A vector can be resolved into rectangular components, along its X- and Y-axis.

• $v_x=v\cos\theta$

$v_y=v\sin\theta$

7. Projectile motion

• When an object is thrown at an angle with the horizontal, it follows a parabolic path under the influence of gravity called Projectile motion.

• Range is the maximum horizontal distance covered during the projectile motion.

$R=\dfrac{u^2\sin (2\theta)}{g}$

• Time of flight is the total time taken by the body to reach back to the ground.

$T=\dfrac{2u\sin (\theta)}{g}$

• The maximum height of the projectile motion is given by,

$R=\dfrac{u^2\sin^2 (\theta)}{2g}$

Where u is the velocity at which the body is projected, θ is the angle of projection and g is the acceleration due to gravity. 

8. Circular motion

• A body is said to be in a circular motion if it undergoes a circular path.

• In a uniform circular motion, speed remains constant.

• The relation between linear velocity (v) and angular velocity (⍵) of a particle moving in a circle of radius r is,

$v=r\omega$

• Angular acceleration is the rate of change of angular velocity with respect to time.

$\alpha=\dfrac{d\omega}{dt}=r\omega^2$

• The relationship between linear acceleration (a) and angular acceleration (α) is

$a=r\alpha$

Important Kinematics Formulas to Learn With Notes

JEE Main formulas are important for doing well in the exam. Using them with organized revision notes becomes useful for understanding everything well. While you go over your JEE Main notes, include the related formulas. First, understand why the formula is used by looking at the notes, then try it on practice problems. This mix helps you understand better, remember more, and get better at solving problems. These are all very important for doing great in JEE Main 2025. You can get the Essential JEE Main Physics Formula PDF for free from Vedantu’s website and get higher scores in your JEE Main 2025 Exams.

Here are some important kinematics formulas based on the current JEE Main syllabus:

1. Position, Displacement, and Distance

Displacement $\Delta x = x_2 - x_1 $

- Distance: Total path covered by the object

2. Average and Instantaneous Velocity

Average Velocity $v_{avg} = \frac{\Delta x}{\Delta t} $

Instantaneous Velocity $ v = \frac{dx}{dt} $

3. Average and Instantaneous Acceleration

Average Acceleration $ a_{avg} = \frac{\Delta v}{\Delta t} $

Instantaneous Acceleration $ a = \frac{dv}{dt} $

4. Equations of Motion (For Constant Acceleration

$ v = u + at $

$ s = ut + \frac{1}{2}at^2 $

$ v^2 = u^2 + 2as $

$ s = \frac{(u + v)}{2} \times t $

Where:  

u = initial velocity  

v = final velocity  

a = acceleration  

s = displacement  

t = time

5. Projectile Motion

Horizontal Range $ R = \frac{u^2 \sin 2\theta}{g} $

Time of Flight $ T = \frac{2u \sin \theta}{g} $

Maximum Height $ H = \frac{u^2 \sin^2 \theta}{2g} $

Where:  

u = initial velocity  

$\theta$ = angle of projection  

g = acceleration due to gravity

6. Relative Motion

Relative Velocity of A with respect to B: $ v_{A/B} = v_A - v_B $

7. Uniform Circular Motion

Angular Velocity $ \omega = \frac{\theta}{t} $

Centripetal Acceleration $ a_c = \frac{v^2}{r} = \omega^2 r $

Where:  

v = linear velocity 

r = radius  

$ \omega $ = angular velocity  

8. Graphical Analysis

Slope of displacement-time graph gives velocity.

The slope of the velocity-time graph gives acceleration.

Area under velocity-time graph gives the displacement.

9. Motion in a Straight Line (Special Cases)

For free fall (when u = 0 ), the equations simplify with g as the acceleration:

v = gt

$s = \frac{1}{2}gt^2$

The Significance of Kinematics Notes for JEE Main 2025

The kinematics chapter explores the mathematical description of motion, focusing on concepts such as displacement, velocity, acceleration, and their relationships. Here are some key features of this chapter:

Introduction to Kinematics:

• Imagine you're tracking a spaceship's journey through the cosmos. Kinematics is your navigation tool, helping you understand its position, velocity, and acceleration without worrying about the forces driving it.

• Think of kinematics as your cosmic GPS, plotting the path of objects through time and space.

The Dance of Displacement:

• Ever wondered how far you've travelled on a roller coaster ride? Displacement has the answer. It's like measuring your journey from where you started to where you ended up.

• Imagine you're an ant on a leaf. If the leaf moves, your displacement changes too!

Velocity: Speed with Direction:

• Velocity is your road map for speed and direction. It tells you how fast you're moving and where you're headed.

• Picture yourself driving a car. Your velocity is how quickly you're going and whether you're cruising north, south, east, or west.

Acceleration: Change in Motion:

• Acceleration is your turbo boost. It's all about how fast you're changing your speed or direction.

• Imagine being on a merry-go-round. If it speeds up or slows down, you're experiencing acceleration.

Time: The Motion Clock:

• Time is the heartbeat of kinematics. It's what ties all the other concepts together. Motion happens over time, and kinematics helps you track it.

• Think of time as the rhythm that sets the pace for your journey through space.

Graphs: Visualizing Motion:

• Graphs are like the photo album of your motion journey. Position-time graphs show how far you've travelled, while velocity-time graphs depict speed changes.

• Imagine plotting your roller coaster adventure on a graph. The ups and downs create a visual story of your motion.

Projectile Adventure: Aim for the Stars:

• Let's launch a water balloon into the sky! Projectile motion helps us predict where it will land. It's like a game of "catch" with gravity.

• Visualize shooting an arrow into the air. The path it takes is a combination of horizontal and vertical motion.

Equations: Solving the Kinematics Puzzle:

• Equations of motion are your tools for solving kinematics puzzles. They help you predict an object's future location, speed, or time in flight.

• Imagine being a detective, using clues (like initial velocity and time) to piece together the motion mystery.

Embark on your Kinematics journey armed with these concepts. It's like having a treasure map to unlock the secrets of motion. Get ready to unravel the mysteries of how things move, from falling leaves to soaring rockets. Your JEE Main success story begins with mastering the dance of kinematics! 

Benefits of learning Kinematics for JEE Mains with Vedantu’s Notes 

• Vedantu’s notes break down Kinematics topics like velocity, acceleration, and motion equations into clear, easy-to-understand sections, saving you time and effort.

• Complex formulas are presented in a straightforward manner, making it easier to memorize and apply them to problems during the exam.

• Created by experienced Vedantu teachers, these notes are crafted specifically to match the JEE syllabus, so you know you're studying relevant material.

• Graph analysis for velocity, displacement, and acceleration is clearly illustrated, which helps you interpret graphs quickly in JEE questions.

• The notes are compact and cover key points, making them ideal for a quick revision right before the exam.

• As downloadable PDFs, you can access these notes on any device, allowing you to study wherever you are, at your convenience.

• Mastering kinematics with Vedantu’s notes lays a strong foundation for future Physics topics, as it's closely linked to other mechanics concepts in the JEE syllabus.

Check These Other Important Links for JEE Main 2025 Kinematics 

Explore additional resources beyond JEE Main 2025 Kinematics notes. Check out these other Useful Links that provide access to learning materials, practice papers, mock tests, and valuable insights. Enhance your preparation, overcome difficulties, and welcome achievement with these resources designed specifically for JEE Main 2025.

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