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Indian Institute of Technology Bombay

If we look around us, we find that there are number of objects which are in motion. An object is said to be in motion if it change its position with the passage of time. In other  words, the movement of an object is known as the motion of the object.
Now observe the following bodies or objects and we will be able to understand the meaning of the term “motion”. Cars, cycles, motorcycles, scooters, buses, rickshaws, trucks etc. running on the road, Birds flying in the sky, Fish swimming in water. All these objects are in motion. Very small objects like atoms and molecules and very large objects like planets, stars and galaxies are in motion.
Thus, all objects ranging from a smallest atom to the largest galaxy are in continuous motion.
Types of Motion :
(A) Linear motion :  A body has linear motion if it moves in a straight line or path.
Ex.    (i) Motion of a moving car on a straight road.
(ii) Motion of a ball dropped from the roof of a building.
(B) Circular (or rotational) Motion : A body has circular motion if it moves around a fixed point.
A vertical passing through the fixed point around which the body moves is known as axis of rotation.
Class 9, Projectile Motion, Acceleration, Speed, Velocity
Ex.    (i) Motion of an electric fan.
(ii) Motion of merry-go-round
(iii) Motion of a spinning top.
(C) Vibratory motion : 
A body has vibratory motion if it moves to and fro about a fixed point.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

Ex.    (i) Motion of a pendulum of a wall clock.
(ii) Motion of a simple pendulum.
MOTION IN LIVING AND NON-LIVING OBJECTS :
It is a common observation that all living objects, whether plants or animals can move in some way or the other.  The motion in animals is more apparent than the motion in plants.
The motion in animals is called LOCOMOTION.
Plants also move but their motion is not apparent as they cannot move from place to place. Their motion takes place in parts. As a plant grows so does its roots and its leaves.
MECHANICS :
The branch of physics which deals with the motion of non-living objects in everyday life is called mechanics or Classical mechanics. It is of two types.

i) Statics and     (ii) Dynamics

STATICS : Statics deals with bodies at rest under the effect of different forces.
DYNAMICS : Dynamics deals with the bodies in motion. It is further of two types :
(i) Kinematics : Kinematics, which is derives from a Greek word kinema meaning motion,is a branch of Physics, which deals with the motion of a body without taking into account the cause of motion.
(ii) Dynamics proper : Dynamics proper, which is derived from a Greek word dyna meaning power it is a branch of Physics, which deals with the motion of bodies by taking into account the cause of motion (force).
Concept of a point object, Rest and motion
Point object : An extended object can be treated as a point object when the distance travelled by the object is much greater than its own size.
“A point object is one, which has no linear dimensions but possesses mass.”
Ex.    (i) Study of motion of a train travelling from Kota to New Delhi.
(ii) Revolution of earth around the sun for one complete revolution.
Rest :– A body is said to be at rest when its position does not change with time respect to the observer.
Motion :– A body is said to be in motion when its position changes with time respect to the observer.

Describe motion :
When a tree, is observed by an observer A sitting on a bench, the tree is at rest. This is because position of the tree is not changing with respect to the observer A.
Class 9, Projectile Motion, Acceleration, Speed, Velocity

Now, When the same tree T is observed by an observer sitting in a superfast train moving with a velocity  n, then the tree is moving with respect to the observer because the position of tree is changing with respect to the observer B.
Rest and motion are relative terms : There is nothing like absolute rest. This means that an object can be at rest and also in motion at the same time i.e. all objects, which are stationary on earth, are said to be at rest with respect to each other, but with respect to the sun are making revolutions at 30 kmh–1. In order to study motion, therefore, we have to choose a fixed position or point with respect to which the motion has to be studied. Such a point or fixed position is called a reference point or the origin. In order to describe the motion of an object we need to keep in mind three things;
(i) The distance of the body from a reference point. This reference point is called the origin of the motion of the body.
(ii) The direction of motion of the body.
(iii) The time of motion.

Scalar and vector quantities
Scalar Quantity :– A quantity that has only magnitude no direction is called a scalar quantity.
Ex.     mass, time, distance, speed, work, power, energy, charge, area, volume, density, pressure, potential, temperature etc.
Vector Quantity :– The physical quantity that has magnitude as well as direction are called vector quantity.
Ex.     velocity, acceleration, force, displacement, momentum, weight, electric field etc.

Differece between scalar & vector quantities :

Scalar quantities Vector quantities
1 These are completely specified by their magnitude only. These are completely specified by their magnitude as well as direction
2 These change by change of their magnitude only These change by change of either their
magnitude or direction or both
3 These are added or subtracted by laws of
ordinary algebra like 4m+5m=9m.
These are added or subtracted by laws of
vector addition.

 DISTANCE AND DISPLACEMENT

Distance : The length of the actual path between the initial and the final position of a moving object in the given time interval is known as the distance travelled by the object.

Class 9, Projectile Motion, Acceleration, Speed, Velocity
Distance = Length of path I (ACB)
Distance is a scalar quantity.

Unit   In SI system : metre (m)
In CGS system : centimetre (cm)
Large unit Kilometre (km)
Displacement:– The shortest distance between the initial position and the final position of a moving object in the given interval of time from initial to the final position of the object is known as the displacement of the object.
Displacement of an object may also be defined as the change in position of the object in a particular direction. That is,

Displacement of an object = Final position – Initial position of the object.
Displacement of an object may be zero but the distance travelled by the object in never zero.
Distance travelled by an object is either equal or greater than the magnitude of displacement of the object.
Displacement = Length of path II (AB) A to B,
displacement is vector quantities.
Units    In SI system : metre (m)
In CGS system : centimetre (cm)

Ex.    A train goes from station A to station B as shown in figure. Calculate
(i)    the distance travelled by the train and
(ii)    the magnitude of the displacement of the train on reaching station B.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

Sol.    (i)    Distance travelled by the train = 50 100 200 400 = 750 km.
(ii)    Magnitude of the displacement in going from station A to station B = 400 km.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

Uniform and non-uniform motion
A moving body may cover equal distances in equal intervals of time or different distances in equal intervals of time. On the basis of above assumption, the motion of a body can be classified as uniform motion and non-uniform motion.
Uniform motion:

Class 9, Projectile Motion, Acceleration, Speed, Velocity

When a body covers equal distances in equal intervals of time, however, small may be time intervals, the body is said to describe a uniform motion.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

Example of uniform motion –
(i)  An aeroplane flying at a speed of 600 km/h
(ii)  A train running at a speed of 120 km/h
(iii) Light energy travelling at a speed of 3 × 108 m/s
(iv)  A spaceship moving at a speed of 100 km/s
Non-uniform motion:

Class 9, Projectile Motion, Acceleration, Speed, Velocity

When a body covers unequal distances in equal intervals of time, the body is said to be moving with a non-uniform motion.

Example of non-uniform motion –
(i)    An aeroplane running on a runway before taking off.
(ii)    A freely falling stone under the action of gravity.
(iii)    An object thrown vertically upward.
(iv)    When the brakes are applied to a moving car.

Speed
Speed of a body is the distance travelled by the body per unit time. or The rate of change of motion is called speed.

(speed = {distance travelled over time taken})
If a body covers a distance S in time t then speed,

(v = {S over t})
Unit : In SI system : m/s or ms–1
In CGS system : cm/s or cms–1
Other km/h or kmh–1

Important note : While comparing the speed of different bodies we must convert all speeds into same units. Speed is a scalar quantity, because it has the magnitude but no direction.

Uniform speed :- When a body covers equal distance in equal intervals of time, the body is to be moving with a uniform speed or constant speed.
Ex.    (i)  A train running with a speed of 120 km/h
(ii) An aeroplane flying with a speed of 600 km/h

Non-uniform speed :- When a body covers unequal distances in equal intervals of time, the body is said to be moving with non-uniform speed or variable speed.

Ex.    (i)   A car running on busy road.
(ii)  An aeroplane landing on runway.

Average speed :- The average speed of the body in a given time interval is defined as the total distance travelled, divided by the time interval.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

Ex. A car travels first half distance with a uniform u and next half distance travels with a uniform speed v. Find its average speed.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

Sol. Total distances = + = d

Total time = t1 + t2 = t

t1 = Class 9, Projectile Motion, Acceleration, Speed, Velocity …(i)

t2 = Class 9, Projectile Motion, Acceleration, Speed, Velocity …(ii)

Vav = Putting the value of equation (i) and (ii)

Vav = Class 9, Projectile Motion, Acceleration, Speed, Velocity = Class 9, Projectile Motion, Acceleration, Speed, Velocity= Class 9, Projectile Motion, Acceleration, Speed, Velocity Class 9, Projectile Motion, Acceleration, Speed, Velocity

Ex. A car travels first half time with a uniform speed u and next half time with a uniform speed v. Find its average speed.

Sol. Class 9, Projectile Motion, Acceleration, Speed, Velocity Class 9, Projectile Motion, Acceleration, Speed, Velocity

Total distances d = + Class 9, Projectile Motion, Acceleration, Speed, Velocity

d = Class 9, Projectile Motion, Acceleration, Speed, Velocity

Total time = T

Average speed = Class 9, Projectile Motion, Acceleration, Speed, Velocity

Vav = Class 9, Projectile Motion, Acceleration, Speed, Velocity= Class 9, Projectile Motion, Acceleration, Speed, Velocity Class 9, Projectile Motion, Acceleration, Speed, Velocity

Instantaneous speed

The speed of a body at any particular instant of time during its motion is called the instantaneous speed of the body.

It is measured by speedometer in vehicles.

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Competitive Window

Comment : It can be very easily argued that

(a) The relative speed between two bodies A and B moving in the same direction with speed |VA| and |VB| i.e.

|Vsame| = difference in the speeds of two bodies A and B = |VA| |VB| or |VB| |VA| … (A)

depending upon the fact whether |VA| > |VB| or |VB| > |VA|

(b) The relative speed between the two bodies A and B moving in the opposite direction with speed |VA| and |VB| i.e.

|Vopposite| = sum of the speed of the two bodies A and B = |VA| + |VB| … (B)

It should be carefully noted that equation A and B are valid only for one-dimensional motion and not in two and three dimension motion.

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Velocity

The velocity of a body is the displacement of a body per unit time.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

The displacement covered by a body per unit time or the speed of a body in specified direction is called the velocity.

Unit: In SI system : m/s or ms_1

In CGS system : cm/s or cms_1

Other km/h or kmh_1, km/min.

Uniform velocity

Class 9, Projectile Motion, Acceleration, Speed, Velocity

When a body covers equal displacement in equal interval of time, the body is said to be moving with a uniform velocity.

Conditions for uniform velocity :_

(i) The body must cover equal displacement in equal intervals of time.

(ii) The direction of motion of the body should not change.

Ex. (i) A train running towards south with a speed of 120 km/h.

(ii) A aeroplane flying due north-east with a speed of 600 km/h.

Very important note :_

Direction of velocity represent direction of motion of body.

OR

Sign of velocity represent the direction of motion of body.

Non-uniform velocity/variable velocity :

Class 9, Projectile Motion, Acceleration, Speed, Velocity

When a body covers unequal displacement in equal intervals of time, the body is said to be moving with variable velocity.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

When a body covers equal distance in equal intervals of time, but its direction changes, then the body is said to be moving with variable velocity.

Conditions for variable velocity :_

(i) It should cover unequal displacement in equal intervals of time.

(ii) It should cover equal distances in equal intervals of time but its direction must change.

Ex. (i) A car running towards north on a busy road has a variable velocity as the displacement covered by it per unit time changes with change in the road condition.

(ii) The blades of a rotating ceiling fan, a person running around a circular track with constant speed etc. are the example of variable velocity, as the direction of the moving body changes in each case.

Average velocity :

Total displacement divided by total time is called an average velocity.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

Vav = Class 9, Projectile Motion, Acceleration, Speed, Velocity

OR

The arithmetic mean of initial velocity and final velocity for a given time period, is called average velocity.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

vav = Class 9, Projectile Motion, Acceleration, Speed, Velocity where u = initial velocity, v = final velocity

Memorise : When a body moves with constant velocity, the average velocity is equal to
instantaneous velocity. The body is said to be in uniform motion.

Difference between Speed and Velocity:

Speed Velocity
It is defined as the rate of change of distance It is the shortest distance between two points
between which the body moves.
It is a scalar quantity It is a vector quantity
It can never be negative or zero It can be negative, zero or positive
Speed is velocity without direction. Velocity is directed speed
Speed may or may not be equal to velocity. A body mass possess different velocities but the same speed.
Speed never decreases with time. For a
moving body it is never zero.
Velocity can decrease with time. For a
moving body it can be zero.
Speed in SI is measured in ms–1 Velocity in SI, is measured in ms–1.

Acceleration

The rate of change of velocity of a moving body with time is called acceleration.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

but change in velocity = final velocity – initial velocity.

Class 9, Projectile Motion, Acceleration, Speed, Velocity

Class 9, Projectile Motion, Acceleration, Speed, Velocity

If body moves with uniform velocity, then v = u and then acceleration is zero i.e. a = o.

Unit of accelration

Acceleration = Class 9, Projectile Motion, Acceleration, Speed, Velocity, Acceleration = Class 9, Projectile Motion, Acceleration, Speed, Velocity, Acceleration = = m/s2

In SI system is m/s2 or ms-2

In CGS system is cm/s2 or cms-2

Positive Acceleration : If the velocity of an object increases with time in the direction of the motion of the object, then the acceleratin of the body is known as positive acceleration.

In this case, the object pick up the speed in a particular direction (i.e., velocity). For example, if an object starts from rest and its velocity goes on increasing with time in the direction of its motion, then the object has positive acceleration. The direction of positive acceleration is in the direction of motion of the object.

Negative Acceleration : If the velocity of an object decreases with time, then the acceleration of the object is known as negative acceleration.

It is written as – Class 9, Projectile Motion, Acceleration, Speed, Velocity

For example, if an object moving with certain velocity is brought to rest then the object is said to have negative acceleration.

Acceleration without changing speed :

When an object moves in a circular path with constant speed, then its velocity changes due to the change in the direction of motion of the object. hence, the object is accelerated without changing its speed.

In this case, the direction of acceleration is towards the centre of the circular path.

  • Positive or negative sign of acceleration always shows the direction of acceleration or direction of force but not represent direction of motion of body.
  • Acceleration which oppose the motion of a body is called retardation or negative acceleration.
  • If sign of velocity and acceleration are same it means speed of body will always increase.
  • If both are opposite sign it means speed of body will always decrease.