## Kinematics Notes PDF in English for Class 11, NEET and JEE Exams

Kinematics Notes PDF: Find below the important notes for the chapter, Kinematics as per the NEET and JEE Physics syllabus. This is helpful for aspirants of NEET and JEE and other exams during last-minute revision. Important notes for Kinematics Notes PDF cover all the important topics and concepts useful for the exam.

## Kinematics Notes PDF

Kinematics is the branch of physics that talks about the description of the motion of bodies. The characteristics of moving bodies like displacement and acceleration will be discussed in this chapter. The fundamental concepts of a motion of a particle in one, as well as two dimensions, will be discussed. Motion can be grouped under categories. The velocity vector is where the point of distinction is made. Based on this, a motion is divided into one dimensional, two-dimensional or three-dimensional.

### Motion in a Straight Line

If an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. Motion in a straight line is nothing but linear motion. As the name suggests, it’s in a particular straight line, thus it can be said that it uses only one dimension.

Types of Linear Motion

The linear motion, also called the Rectilinear Motion can be of two types:

• Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line and covers an equal amount of distance in an equal interval of time, it is said to have uniform motion. In simple words, a body is said to have uniform acceleration if the rate of change of its velocity remains constant. Example: If a car travels at a speed of 60 km/hour, it will cover a 1 km/minute. In this sense, the motion of car acceleration is uniform.
• Non-Uniform linear motion with variable velocity or non-zero acceleration: Unlike the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time—the rate of change of its velocity changes at different points of time during its movement. Example: A boy is kicking a football. It might cover 4 meters in the first attempt, 6 meters in the second change, 9 meters in the third attempt and so on as per the velocity exerted by the boy.

Motion in a Straight Line Formulas

 v =u + at s= ut+ 1/2 at2 v2 = u2 + 2as

Frame of reference

The motion of a particle is always described with respect to a reference system. A reference system is made by taking an arbitrary point as origin and imagining a co-ordinate system to be attached to it. This co-ordinate system chosen for a given problem constitutes the reference system for it. We generally choose a co-ordinate system attached to the earth as the reference system for most of the problems.

Path Length

The path length is the total length of the path that has to be traversed by the object. For a particle in motion the total length of the actual path traversed between initial and final positions of the particle is known as the ‘total path length’ or distance covered by it.

Displacement

Displacement of a particle in a given time is defined as the change in the position of particle in a particular direction during that time. It is given by a vector drawn from its initial position to its final position.
Factors Distinguishing Displacement from Distance:
—> Displacement has direction. Distance does not have direction.
—> The magnitude of displacement can be both positive and negative.
—> Distance is always positive. It never decreases with time.
—> Distance ≥ | Displacement |

Uniform Motion

When the displacement of an object is equal in equal time intervals, the motion is said to be uniform, else it is referred to as non-uniform.

Average Speed

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction. Let us know how to calculate average speed, the average speed formula, and solved examples on average speed.

Instantaneous Velocity

It is the velocity when the limit of the average velocity has an indefinitely smaller interval of time. Instantaneous Velocity Formula is made use of to determine the instantaneous velocity of the given body at any specific instant. It is articulated as:

Average Acceleration

It is the change in velocity corresponding to the time interval with in which the change has accelerated.

Velocity and Acceleration

The velocity of the object is defined as the displacement by the time taken. It is a vector quantity, and it has both magnitude and direction. The rate of change of velocity is called acceleration.

Motion Graph

There are three types of motion graphs that are studied in kinematics.

1. Displacement – time graph

2. Velocity – time graph

3. Acceleration – time graph

Motion Diagram

The pictorial representation of the motion of the object is called the motion diagram. In the same diagram, various positions of the object at equally spaced intervals are represented in a motion diagram. From the diagram we can see if the object has accelerated, retarded or at rest. We can understand that the object is getting accelerated if there is an increase in the space between the objects as time passes, and the object is getting retarded if the space between the object decreases with time.

Kinematic Equations

There are four kinematic equations when the initial starting point is taken as the origin, and the acceleration of the object is constant.

1. v = v0 + at

2. d = (½) (v0 + v)t

3. d = v0t + (at2/2)

4. v2 = v02 + 2ad

v is the final velocity

v0 is the initial velocity

a is the constant acceleration

t is the time interval

d is the displacement

Each of the above equations has only four of the five variables. If we know the value of three variables in an equation, the fourth variable can be determined.

Rotational Kinematics Equations

In the translational motion, we saw there are five important variables. Each of these variables will have a corresponding variable in rotational motion. The position variable x is replaced by the angle θ in a rotational motion. The initial and the final velocity is given by the angular velocity(ω), and it is measured in radians per second. The acceleration is replaced by the angular acceleration (α), which describes the rate of change of angular velocity with respect to time. Angular acceleration is measured in radians per second square. The time is represented as t even in rotational motion. The rotational kinematics equations are

1. ω = ω0 + αt

2. θ = θ0 + (½) (ω0 + ω)t

3. θ = θ0 + ω0t + (αt2/2)

4. ω 2 = ω02 + 2α (θ – θ0)

Kinematics Formulas for Projectile Motion

Imagine a projectile motion as presented in the figure.Thus, the kinematics formulas are:

In x-direction:

vx = vxo

x = xo + vxo

In y-direction:

vy = vyo – gt

y = yo + vyot –1212 gt2

vy2 = vyo2 – 2g(y – yo)

Kinematical Graphs

The ‘displacement-time’ and the ‘velocity-time’ graphs of a particle are often used to provide us with a visual representation of the motion of a particle. The ‘shape’ of the graphs depends on the initial ‘co-ordinates’ and the ‘nature’ of the acceleration of the particle (Fig.)

The following general results are always valid

• The slope of the displacement-time graph at any instant gives the speed of the particle at that instant.
• The slope of the velocity-time graph at any instant gives the magnitude of the acceleration of the particle at that instant.
• The area enclosed by the velocity-time graph, the time-axis and the two co-ordinates at ,time instants t1 to t2 gives the distance moved by the particle in the time-interval from t1 to t2.

Uniform Motion

• If a body is said to be in uniform motion, the body completes equal distances in equal intervals of time.

• Here, velocity is constant during the course of motion.

• Also, acceleration is zero during the course of motion.

Non-Uniform Motion

• If a body undergoes non-uniform motion, the body is said to be in uniformly accelerated motion.

• Here, the magnitude of velocity increases or decreases with the passage of time.

• Also, acceleration would not be zero as it undergoes accelerated motion.

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