kinetics motin in one dimension

Basics Of Physics Engr: Kashif Ali Magsi 1

Mechanics

It deals with conditions under which objects remain at rest and motion of bodies with and without the influences of any force. The study of mechanics is divided into three parts

i) Statics

It deals with bodies at rest under the action of forces In statics the time factor does not play any role.

ii) Kinematics

The word kinematics is derived from the Greek word kinema meaning “motion”.

It does not consider the cause size, shape, mass etc. of the body; it is restricted to properties of motion.

This is related with the classification and comparison of motions Kinematics is the study of how things move – how far (distance and

displacement), how fast (speed and velocity), and how fast changes (acceleration) but it does not answer as to why it is moving in that particular way.

Thus kinematics deals only with the space-time relationships for a moving body.

Kinematics is the study of the relationships between distance and displacement, speed and velocity, acceleration, and time.

iii) Dynamics

The word dynamics is derived from Greek word dynamis meaning “power”. Dynamics is the study of why things move. It deals with the cause of motion. Or the effect of forces in causing motion.

Therefore, mass of the object must be considered.

Mechanics

Statics Kinematic Dynamics


It provides not only the description of motion but also gives explanation for the way the motion takes place.

The dynamic description of motion involves terms like force, momentum, impulse etc.

Rest and Motion

i) Rest An object is said to be at rest if it does not change its position w. r. t. its surroundings with the passage of time. i.e. a book laying on the desk, a boy sitting chair etc.

Rest is of two types:

i) Absolute rest: Complete absence of motion. It is impossible to obtain.

ii) Relative rest: When a body does not change its position with respect to another

one, then it is said to be in relative rest.

ii) Motion

An object is said to be in motion if it changes its position with respect to its

surroundings in given time.

Motion is always observed and measured with a point of reference.

All livings things show motion whereas non- living things show motion when

some force is acting on it.

i.e. A bird flying in air, a train moving on track etc.

Rest and motion are relative. Rest and motion are relative terms. For example, a book on the table is at rest

w.r.t. table and other objects in the rom. But all these objects are sharing the motion of the earth. If an observer is located on the moon, he will observe that the book and other objects in the room are moving. Thus the book is at rest if viewed from the room but is moving if viewed from the moon.


Types of Motion

i) Translational Motion

A body is said to have translational motion if each particle of the body has the same displacement in the same time interval.

In this type of motion, every particle of body covers a definite times in linear paths.

The motion of the object is said to be purely translational if the axis of the frame of reference of the object remains always parallel to the corresponding axes of observer’s frame of reference.

In a translational motion the object may not be necessarily moving along a straight line.

EXAMPLE: (i) Motion of a person on a road. (ii) Motion of a car or truck on a road.

Types of the translator motion

a) Rectilinear Motion

A linear motion in which the direction of the velocity remains constant and the path is a straight line.

If the body moves so that every particle of the body follows a straight-line path, then the motion of the body is

Motion

Translational Motion

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Rotational motion

Oscillatory Motion

Translational Motion

Rectilinear Motion Curvilinear Motion


said to be rectilinear. If the center of mass of the body moves along a straight line connecting points

A and B, then the motion of the center of mass of the body is rectilinear. EXAMPLE: (i) The lift moving up or down (ii) The man sliding a box along the straight line. b) Curvilinear motion

Curvilinear motion is defined as motion that occurs when a particle travels along a curved path.

The curved path can be in two dimensions (in a plane), or in three dimensions.

This type of motion is more complex than rectilinear (straight-line) motion.

EXAMPLE: (i)Throwing paper airplanes (ii)A stone thrown into the air at an angle ii) Rotational motion

A body is said to have rotational motion if each particle of the body (except those on the axis of rotation) travels in a circle.

The axis of rotation is a straight line that consists of the centers of the circular motion of the particles.

If a single particle or a point mass moves in a circle, it is called circular motion.

EXAMPLE: (i) Motion of wheel (ii) Motion of the blades of a fan iii) Oscillatory Motion

A body is said to have an oscillatory motion if it moves to and fro repeatedly about a fixed point called mean position.

If the amplitude of oscillatory motion is extremely small, the motion is called vibratory motion.


EXAMPLE: (i) Motion of simple pendulum (ii) Motion of the wires of guitar (iii) Motion of swing Types of Motion with respect to changes in Velocity i) Uniform motion

If velocity does not change with respect to time then it is called uniform velocity

Uniform motion is the kind of motion in which a body covers equal distances in equal intervals of time. It does not matter how small the time intervals are, as long as the distances covered are equal.

If a body is involved in rectilinear motion and the motion is uniform, then the acceleration of the body must be zero.

Planets move around the sun in uniform motion In uniform motion does not depend upon the choice of origin.

ii) Non- uniform motion

Non Uniform motion on the other hand is the kind of motion in which a body cover unequal distances in equal distances of time, no matter how small the time intervals.

If a body is involved in rectilinear motion, and if the motion is non-uniform, then the acceleration of the body must be non-zero.

A freely ball from a certain height covers unequal distances in equal intervals of time, so its motion is non-uniform.

Non uniform motion is also called accelerated motion. Now, students usually do confuse uniform motion with uniform acceleration.

If a body is having some uniform or constant acceleration (in rectilinear motion), it means that the body’s speed is changing every second, which means the motion can’t be uniform.


Concept of point object

An object is said to be a point object if it changes its position by distances which are much greater than its size. Examples: (i) Let us consider the revolution of Earth around the Sun. The diameter of the earth is very small as compared to the length of its orbit around the Sun. So, Earth can be regarded as a point object. (ii) A car travelling a few hundred kilometers may be regarded as a point object.

Frame of reference

The place from which motion is observed and

measured is called frame of reference. In order to measure motion (i. e to locate the

position of an object), we need a coordinate system. Tis coordinate m is attached to some specified body, usually earth’s surface. Unless stated otherwise, frame of reference means coordinate system attached to earth.

Distance and Displacement

i) Distance The total length of the path travelled by an object during a given time is called

the distance. It is a scalar quantity. Its S.I unit is meter. The value of distance cannot be negative.

ii) Displacement

The shortest distance from the initial position to the final position of an object is called displacement of object.

It is vector quantity and is always directed from the initial point to the terminal point.

The displacement is measured in meters in SI units. Its value can be positive and negative.


Displacement is not affected by shift of position of the origin of the coordinate axis.

Displacement of an object does not tell us about the path followed by the object.

Speed

Speed indicates how fast something is moving. The speed of a moving object is defined as the total distance covered by thr

time taken to cover the distance.

Speed = Total distance covered

Time taken

The SI unit of speed is meter per second, m/s. Speed is scalar quantity The speed of an object can be positive or zero but not negative. It is because

distance cannot be negative.

Types of Speed i) Uniform Speed

An object is said to be moving with a uniform speed (i.e. constant speed) if it covers equal distances in equal intervals of time, however small these time intervals may be.

ii) Variable Speed

An object is said to be moving with a variable speed if it covers equal distances in unequal intervals of time.

iii) Average Speed

When an object moves with a variable speed, we generally describe its motion in terms of average speed.

The average speed of an object is the total distance covered divided by time taken to cover the distance,

Average Speed = Total distance covered

Time taken


iv) Instantaneous speed When an object is moving with a variable speed, it has different speed at

different instants of time. The speed of an object at a given instant of time is called its instantaneous

speed.

Velocity

It tells us how fast and in which direction it is moving. The velocity of a moving object is defined the displacement divided by the

time taken to cover the distance.

Velocity = Displacement

Time taken

The SI unit of velocity is meter per second, m/s. Velocity is vector quantity The direction of velocity is the same as that of displacement. Since the displacement can be zero, positive or negative, the velocity of an

object may be positive, zero or negative. Types of Velocity i) Uniform Velocity

An object is said to be moving with a uniform velocity (i.e. Constant velocity) if it undergoes equal displacement in equal intervals of time, however small these time intervals may be.

Uniform velocity means that magnitude as well as direction of the velocity remains constant.

When the average velocity of an object is equal to its instantaneous velocity it becomes uniform velocity.

It is on a straight line path and always in the same direction. Acceleration is zero. Net force is zero.

ii) Variable Velocity

An object is said to be moving with a variable velocity (Non- Uniform velocity) if there is change in its magnitude or direction or both.

A body moving with a constant speed in a circle has a variable velocity.


Although speed (magnitude of velocity) is constant, the direction of velocity of the body is changing from instant to instant.

iii) Average Velocity

When an object moves with a variable Velocity, we generally describe its motion in terms of average velocity.

The average speed of an object is the total distance covered divided by time taken to cover the distance,

Average velocity = Displacement

Time taken

iv)Instantaneous Velocity

When an object is moving with a variable velocity, it has different velocity at different instants of time.

The velocity of an object at a given instant of time is called its instantaneous velocity.

Acceleration

The acceleration of a moving object is defined as the change in velocity divided by the time taken for the change in velocity

Acceleration = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

𝑇𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙

The SI unit of acceleration is m/s2. Acceleration is a vector quantity. The direction of the acceleration is the same as that of the velocity. The acceleration is positive if the velocity is increasing and is negative if the

velocity is decreasing. The negative acceleration is also called retardation of deceleration.

Types of Acceleration i) Uniform Acceleration

An object is said to be moving with a uniform acceleration (i.e. constant acceleration) if its velocity changes by equal amounts in equal amounts in


equal intervals of time, however small these time intervals may be. Uniform acceleration means that magnitude as well as direction of the

acceleration remains constant. When the average acceleration of an object is equal to its instantaneous

acceleration it becomes uniform acceleration. ii) Variable acceleration

An object is said to be moving with a variable acceleration (Non- Uniform acceleration) if there is change in its magnitude or direction or both.

iii) Average Acceleration

The average acceleration of an object is defined as the change in velocity divided by time interval for the change in velocity

Average velocity = V1−V2

t2−t1 = V/t

Types of Motion with respect to changes in acceleration (i ) Accelerated motion motion with a continually increasing velocity. Any acceleration of an object necessarily implies a net force in the direction of acceleration. A freely ball from a certain height covers unequal distances in equal intervals of time, so its motion called as accelerated motion. There are two types of Accelerated motion


(a) Uniform Acceleration motion

Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an equal amount in every equal time period.

Uniformly accelerated motion is motion with a constant, uniform change in velocity. This often, but does not always, include a change in speed.

(b) Non Uniform acceleration Motion

When an object is moving with a variable acceleration (Non- Uniform acceleration) if there is change in its magnitude or direction or both. That motion is called as non- uniform acceleration motion.

(ii) Non Acceleration Motion

Non accelerated motion is when a body is in motion but no force is acting on it to either speed it up or slow down hence the velocity is constant.

Equation of Motion

Kinematic equations provide a useful means of determining the value of an

unknown motion parameter if three motion parameters are known. In the

case of a free-fall motion, the acceleration is often known.

FIRST Equation of Motion

𝐕𝒇= 𝐕𝒊+at

Consider a body initial moving with velocity "Vi". After certain interval of time "t",

its velocity becomes "Vf". Now

Change in velocity = Vf - Vi

OR

� V =V𝑓 – V𝑖

Due to change in velocity, acceleration "a" is produced in the body. Acceleration is


given by

a = � V/t

Putting the value of "� V"

a = (V𝑓 – V𝑖)

𝑡

at = V𝑓 – V𝑖

𝐕𝒇= 𝐕𝒊+at

SECOND EQUATION OF MOTION

OR

S = 𝐕𝒊t + 𝟏

𝟐at2

Consider a car moving on a straight road with an initial velocity equal to ‘Vi’. After an

interval of time ‘t’ its velocity becomes ‘Vf’. Now first we will determine the average

velocity of body.

Average velocity = (𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 + 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦)

2

OR

Vav = (𝑉𝑖 + 𝑉𝑓)

2

but Vf = Vi + at

Putting the value of Vf

Vav = (𝑉𝑖 + 𝑉𝑖 + 𝑎𝑡)

2

Vav = (2𝑉𝑖 + 𝑎𝑡)

2


Vav = 2𝑉𝑖

2 +

𝑎𝑡

2

Vav = Vi + 𝑎𝑡

2

Vav = Vi + 1

2at....................................... (i)

We know that

S = Vav x t

Putting the value of ‘Vav’

S = [Vi + 1

2at] t

THIRD EQUATION OF MOTION

OR

2aS = Vf 2 – Vi 2

Initial velocity, final velocity, acceleration, and distance are related in third equation

of motion.

Consider a body moving initially with velocity ‘Vi’. After certain interval of time its

velocity becomes ‘Vf’. Due to change in velocity, acceleration ‘a’ is produced in the

body. Let the body travels a distance of ‘s’ meters.

According to first equation of motion:

V𝑓= V𝑖+at

OR

Vf – Vi = at

OR


t =(V𝑓 – V𝑖)

𝑎.................... (i)

Average velocity of body is given by:

Average velocity = (𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 + 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦)

2

Vav = (𝑉𝑖 + 𝑉𝑓)

2.................. (ii)

We know that :

S = Vav x t.................. (ii)

Putting the value of Vav and t from equation (i) and (ii) in equation (iii)

S = { (𝑉𝑓 + 𝑉𝑖)

2} {

(𝑉𝑓 – 𝑉𝑖)

𝑎}

2aS = (Vf + Vi)(Vf – Vi)

According to [ (a+b)(a-b)=a2-b2]

2aS = Vf 2 – Vi 2

Free Fall Motion

A free falling object is an object that is falling under the sole influence of

gravity. Any object that is being acted upon only by the force of gravity is said

to be in a state of free fall. There are two important motion characteristics that

are true of free-falling objects:

1. Free-falling objects do not encounter air resistance.

2. All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s

(often approximated as 10 m/s/s for back-of-the-envelope calculations)

The remarkable observation that all free falling objects fall at the same rate

was first proposed by Galileo, nearly 400 years ago.

There are a few conceptual characteristics of free fall motion that will be of


value when using the equations to analyze free fall motion. These concepts are

described as follows:

An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign

indicates a downward acceleration.) Whether explicitly stated or not, the

value of the acceleration in the kinematic equations is -9.8 m/s/s for any

freely falling object.

If an object is merely dropped (as opposed to being thrown) from an elevated

height, then the initial velocity of the object is 0 m/s.

If an object is projected upwards in a perfectly vertical direction, then it will

slow down as it rises upward. The instant at which it reaches the peak of its

trajectory, its velocity is 0 m/s. This value can be used as one of the motion

parameters in the kinematic equations; for example, the final velocity (vf)

after traveling to the peak would be assigned a value of 0 m/s.

If an object is projected upwards in a perfectly vertical direction, then the

velocity at which it is projected is equal in magnitude and opposite in sign to

the velocity that it has when it returns to the same height. That is, a ball

projected vertically with an upward velocity of +30 m/s will have a

downward velocity of -30 m/s when it returns to the same height.

Equation of motion due to free fall Motion

i) 𝐕𝒇= 𝐕𝒊+gt

ii) S = 𝐕𝒊t + 𝟏

𝟐gt2

iii) 2gS = Vf 2 – Vi 2

kinetics motin in one dimension

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