NCERT Textbook: Motion - Science & Technology for UPSC CSE

 Page 1


In everyday life, we see some objects at rest
and others in motion. Birds fly, fish swim,
blood flows through veins and arteries and
cars move. Atoms, molecules, planets, stars
and galaxies are all in motion. We often
perceive an object to be in motion when its
position changes with time. However, there
are situations where the motion is inferred
through indirect evidences. For example, we
infer the motion of air by observing the
movement of dust and the movement of leaves
and branches of trees. What causes the
phenomena of sunrise, sunset and changing
of seasons? Is it due to the motion of the
earth? If it is true, why don’t we directly
perceive the motion of the earth?
An object may appear to be moving for
one person and stationary for some other. For
the passengers in a moving bus, the roadside
trees appear to be moving backwards. A
person standing on the road–side perceives
the bus alongwith the passengers as moving.
However, a passenger inside the bus sees his
fellow passengers to be at rest. What do these
observations indicate?
Most motions are complex. Some objects
may move in a straight line, others may take
a circular path. Some may rotate and a few
others may vibrate. There may be situations
involving a combination of these. In this
chapter, we shall first learn to describe the
motion of objects along a straight line. We
shall also learn to express such  motions
through simple equations and graphs. Later,
we shall discuss ways of describing circular
motion.
Activity ______________8.1
? Discuss whether the walls of your
classroom are at rest or in motion.
Activity ______________8.2
? Have you ever experienced that the
train in which you are sitting appears
to move while it is at rest?
? Discuss and share your experience.
Think and Act
We sometimes are endangered by the
motion of objects around us, especially
if that motion is erratic and
uncontrolled as observed in a flooded
river , a hurricane or a tsunami. On the
other hand, controlled motion can be a
service to human beings such as in the
generation of hydro-electric power. Do
you feel the necessity to study the
erratic motion of some objects and
learn to control them?
8.1 Describing Motion
We describe the location of an object by
specifying a reference point. Let us
understand this by an example. Let us
assume that a school in a village is 2 km north
of the railway station. We have specified the
position of the school with respect to the
railway station. In this example, the railway
station is the reference point. We could have
also chosen other reference points according
to our convenience. Therefore, to describe the
position of an object we need to specify a
reference point called the origin.
8 8
8 8 8
M M M M MOTION OTION OTION OTION OTION
Chapter
Page 2


In everyday life, we see some objects at rest
and others in motion. Birds fly, fish swim,
blood flows through veins and arteries and
cars move. Atoms, molecules, planets, stars
and galaxies are all in motion. We often
perceive an object to be in motion when its
position changes with time. However, there
are situations where the motion is inferred
through indirect evidences. For example, we
infer the motion of air by observing the
movement of dust and the movement of leaves
and branches of trees. What causes the
phenomena of sunrise, sunset and changing
of seasons? Is it due to the motion of the
earth? If it is true, why don’t we directly
perceive the motion of the earth?
An object may appear to be moving for
one person and stationary for some other. For
the passengers in a moving bus, the roadside
trees appear to be moving backwards. A
person standing on the road–side perceives
the bus alongwith the passengers as moving.
However, a passenger inside the bus sees his
fellow passengers to be at rest. What do these
observations indicate?
Most motions are complex. Some objects
may move in a straight line, others may take
a circular path. Some may rotate and a few
others may vibrate. There may be situations
involving a combination of these. In this
chapter, we shall first learn to describe the
motion of objects along a straight line. We
shall also learn to express such  motions
through simple equations and graphs. Later,
we shall discuss ways of describing circular
motion.
Activity ______________8.1
? Discuss whether the walls of your
classroom are at rest or in motion.
Activity ______________8.2
? Have you ever experienced that the
train in which you are sitting appears
to move while it is at rest?
? Discuss and share your experience.
Think and Act
We sometimes are endangered by the
motion of objects around us, especially
if that motion is erratic and
uncontrolled as observed in a flooded
river , a hurricane or a tsunami. On the
other hand, controlled motion can be a
service to human beings such as in the
generation of hydro-electric power. Do
you feel the necessity to study the
erratic motion of some objects and
learn to control them?
8.1 Describing Motion
We describe the location of an object by
specifying a reference point. Let us
understand this by an example. Let us
assume that a school in a village is 2 km north
of the railway station. We have specified the
position of the school with respect to the
railway station. In this example, the railway
station is the reference point. We could have
also chosen other reference points according
to our convenience. Therefore, to describe the
position of an object we need to specify a
reference point called the origin.
8 8
8 8 8
M M M M MOTION OTION OTION OTION OTION
Chapter
8.1.1 MOTION ALONG A STRAIGHT LINE
The simplest type of motion is the motion
along a straight line. We shall first learn to
describe this by an example. Consider the
motion of an object moving along a straight
path. The object starts its journey from O
which is treated as its reference point
(Fig. 8.1). Let A, B and C represent the
position of the object at different instants. At
first, the object moves through C and B and
reaches A. Then it moves back along the same
path and reaches C through B.
displacement, are used to describe the overall
motion of an object and to locate its final
position with reference to its initial position
at a given time.
Activity ______________8.3
? Take a metre scale and a long rope.
? Walk from one corner of a basket-ball
court to its oppposite corner along its
sides.
? Measure the distance covered by you
and magnitude of the displacement.
? What difference would you notice
between the two in this case?
Activity ______________8.4
? Automobiles are fitted with a device
that shows the distance travelled. Such
a device is known as an odometer. A
car is driven from Bhubaneshwar to
New Delhi. The difference between the
final reading and the initial reading of
the odometer is 1850 km.
? Find the magnitude of the displacement
between Bhubaneshwar and New Delhi
by using the Road Map of India.
The total path length covered by the object
is OA + AC, that is 60 km + 35 km = 95 km.
This is the distance covered by the object. To
describe distance we need to specify only the
numerical value and not the direction of
motion. There are certain quantities which
are described by specifying only their
numerical values. The numerical value of a
physical quantity is its magnitude. From this
example, can you find out the distance of the
final position C of the object from the initial
position O? This difference will give you the
numerical value of the displacement of the
object from O to C through A. The shortest
distance measured from the initial to the final
position of an object is known as the
displacement.
Can the magnitude of the displacement
be equal to the distance travelled by an
object? Consider the example given in
(Fig. 8.1). For motion of the object from O to
A,  the distance covered is 60 km  and the
magnitude of displacement is also 60 km.
During its motion from O to A and back to B,
the distance covered = 60 km + 25 km = 85 km
Fig. 8.1: Positions of an object on a straight line path
while the magnitude of displacement = 35 km.
Thus, the magnitude of displacement (35 km)
is not equal to the path length (85 km).
Further, we will notice that the magnitude of
the displacement for a course of motion may
be zero but the corresponding distance
covered is not zero. If we consider the object
to travel back to O, the final position concides
with the initial position, and therefore, the
displacement is zero. However, the distance
covered in this journey is OA + AO = 60 km +
60 km = 120 km. Thus, two different physical
quantities — the distance and the
MOTION 99
Page 3


In everyday life, we see some objects at rest
and others in motion. Birds fly, fish swim,
blood flows through veins and arteries and
cars move. Atoms, molecules, planets, stars
and galaxies are all in motion. We often
perceive an object to be in motion when its
position changes with time. However, there
are situations where the motion is inferred
through indirect evidences. For example, we
infer the motion of air by observing the
movement of dust and the movement of leaves
and branches of trees. What causes the
phenomena of sunrise, sunset and changing
of seasons? Is it due to the motion of the
earth? If it is true, why don’t we directly
perceive the motion of the earth?
An object may appear to be moving for
one person and stationary for some other. For
the passengers in a moving bus, the roadside
trees appear to be moving backwards. A
person standing on the road–side perceives
the bus alongwith the passengers as moving.
However, a passenger inside the bus sees his
fellow passengers to be at rest. What do these
observations indicate?
Most motions are complex. Some objects
may move in a straight line, others may take
a circular path. Some may rotate and a few
others may vibrate. There may be situations
involving a combination of these. In this
chapter, we shall first learn to describe the
motion of objects along a straight line. We
shall also learn to express such  motions
through simple equations and graphs. Later,
we shall discuss ways of describing circular
motion.
Activity ______________8.1
? Discuss whether the walls of your
classroom are at rest or in motion.
Activity ______________8.2
? Have you ever experienced that the
train in which you are sitting appears
to move while it is at rest?
? Discuss and share your experience.
Think and Act
We sometimes are endangered by the
motion of objects around us, especially
if that motion is erratic and
uncontrolled as observed in a flooded
river , a hurricane or a tsunami. On the
other hand, controlled motion can be a
service to human beings such as in the
generation of hydro-electric power. Do
you feel the necessity to study the
erratic motion of some objects and
learn to control them?
8.1 Describing Motion
We describe the location of an object by
specifying a reference point. Let us
understand this by an example. Let us
assume that a school in a village is 2 km north
of the railway station. We have specified the
position of the school with respect to the
railway station. In this example, the railway
station is the reference point. We could have
also chosen other reference points according
to our convenience. Therefore, to describe the
position of an object we need to specify a
reference point called the origin.
8 8
8 8 8
M M M M MOTION OTION OTION OTION OTION
Chapter
8.1.1 MOTION ALONG A STRAIGHT LINE
The simplest type of motion is the motion
along a straight line. We shall first learn to
describe this by an example. Consider the
motion of an object moving along a straight
path. The object starts its journey from O
which is treated as its reference point
(Fig. 8.1). Let A, B and C represent the
position of the object at different instants. At
first, the object moves through C and B and
reaches A. Then it moves back along the same
path and reaches C through B.
displacement, are used to describe the overall
motion of an object and to locate its final
position with reference to its initial position
at a given time.
Activity ______________8.3
? Take a metre scale and a long rope.
? Walk from one corner of a basket-ball
court to its oppposite corner along its
sides.
? Measure the distance covered by you
and magnitude of the displacement.
? What difference would you notice
between the two in this case?
Activity ______________8.4
? Automobiles are fitted with a device
that shows the distance travelled. Such
a device is known as an odometer. A
car is driven from Bhubaneshwar to
New Delhi. The difference between the
final reading and the initial reading of
the odometer is 1850 km.
? Find the magnitude of the displacement
between Bhubaneshwar and New Delhi
by using the Road Map of India.
The total path length covered by the object
is OA + AC, that is 60 km + 35 km = 95 km.
This is the distance covered by the object. To
describe distance we need to specify only the
numerical value and not the direction of
motion. There are certain quantities which
are described by specifying only their
numerical values. The numerical value of a
physical quantity is its magnitude. From this
example, can you find out the distance of the
final position C of the object from the initial
position O? This difference will give you the
numerical value of the displacement of the
object from O to C through A. The shortest
distance measured from the initial to the final
position of an object is known as the
displacement.
Can the magnitude of the displacement
be equal to the distance travelled by an
object? Consider the example given in
(Fig. 8.1). For motion of the object from O to
A,  the distance covered is 60 km  and the
magnitude of displacement is also 60 km.
During its motion from O to A and back to B,
the distance covered = 60 km + 25 km = 85 km
Fig. 8.1: Positions of an object on a straight line path
while the magnitude of displacement = 35 km.
Thus, the magnitude of displacement (35 km)
is not equal to the path length (85 km).
Further, we will notice that the magnitude of
the displacement for a course of motion may
be zero but the corresponding distance
covered is not zero. If we consider the object
to travel back to O, the final position concides
with the initial position, and therefore, the
displacement is zero. However, the distance
covered in this journey is OA + AO = 60 km +
60 km = 120 km. Thus, two different physical
quantities — the distance and the
MOTION 99 SCIENCE 100
uestions
1. An object has moved through a
distance. Can it have zero
displacement? If yes, support
your answer with an example.
2. A farmer moves along the
boundary of a square field of side
10 m in 40 s. What will be the
magnitude of displacement of the
farmer at the end of 2 minutes
20 seconds?
3. Which of the following is true for
displacement?
(a) It cannot be zero.
(b) Its magnitude is greater than
the distance travelled by the
object.
8.1.2 UNIFORM MOTION AND NON-
UNIFORM MOTION
Consider an object moving along a straight
line. Let it travel 50 km in the first hour,
50 km more in the second hour, 50 km in the
third hour and 50 km in the fourth hour. In
this case, the object covers 50 km in each
hour. As the object covers equal distances in
equal intervals of time, it is said to be in
uniform motion.  The time interval in this
motion may be small or big. In our
day-to-day life, we come across motions where
objects cover unequal distances in equal
intervals of time, for example, when a car is
moving on a crowded street or a person is
jogging in a park. These are some instances
of non-uniform motion.
Activity ______________8.5
? The data regarding the motion of two
different objects A and B are given in
Table 8.1.
? Examine them carefully and state
whether the motion of the objects is
uniform or non-uniform.
Q
(a)
(b)
Fig. 8.2
Table 8.1
Time Distance Distance
travelled by travelled by
object A in m object  B in m
9:30 am 10 12
9:45 am 20 19
10:00 am 30 23
10:15 am 40 35
10:30 am 50 37
10:45 am 60 41
11:00 am 70 44
8.2 Measuring the Rate of Motion
Page 4


In everyday life, we see some objects at rest
and others in motion. Birds fly, fish swim,
blood flows through veins and arteries and
cars move. Atoms, molecules, planets, stars
and galaxies are all in motion. We often
perceive an object to be in motion when its
position changes with time. However, there
are situations where the motion is inferred
through indirect evidences. For example, we
infer the motion of air by observing the
movement of dust and the movement of leaves
and branches of trees. What causes the
phenomena of sunrise, sunset and changing
of seasons? Is it due to the motion of the
earth? If it is true, why don’t we directly
perceive the motion of the earth?
An object may appear to be moving for
one person and stationary for some other. For
the passengers in a moving bus, the roadside
trees appear to be moving backwards. A
person standing on the road–side perceives
the bus alongwith the passengers as moving.
However, a passenger inside the bus sees his
fellow passengers to be at rest. What do these
observations indicate?
Most motions are complex. Some objects
may move in a straight line, others may take
a circular path. Some may rotate and a few
others may vibrate. There may be situations
involving a combination of these. In this
chapter, we shall first learn to describe the
motion of objects along a straight line. We
shall also learn to express such  motions
through simple equations and graphs. Later,
we shall discuss ways of describing circular
motion.
Activity ______________8.1
? Discuss whether the walls of your
classroom are at rest or in motion.
Activity ______________8.2
? Have you ever experienced that the
train in which you are sitting appears
to move while it is at rest?
? Discuss and share your experience.
Think and Act
We sometimes are endangered by the
motion of objects around us, especially
if that motion is erratic and
uncontrolled as observed in a flooded
river , a hurricane or a tsunami. On the
other hand, controlled motion can be a
service to human beings such as in the
generation of hydro-electric power. Do
you feel the necessity to study the
erratic motion of some objects and
learn to control them?
8.1 Describing Motion
We describe the location of an object by
specifying a reference point. Let us
understand this by an example. Let us
assume that a school in a village is 2 km north
of the railway station. We have specified the
position of the school with respect to the
railway station. In this example, the railway
station is the reference point. We could have
also chosen other reference points according
to our convenience. Therefore, to describe the
position of an object we need to specify a
reference point called the origin.
8 8
8 8 8
M M M M MOTION OTION OTION OTION OTION
Chapter
8.1.1 MOTION ALONG A STRAIGHT LINE
The simplest type of motion is the motion
along a straight line. We shall first learn to
describe this by an example. Consider the
motion of an object moving along a straight
path. The object starts its journey from O
which is treated as its reference point
(Fig. 8.1). Let A, B and C represent the
position of the object at different instants. At
first, the object moves through C and B and
reaches A. Then it moves back along the same
path and reaches C through B.
displacement, are used to describe the overall
motion of an object and to locate its final
position with reference to its initial position
at a given time.
Activity ______________8.3
? Take a metre scale and a long rope.
? Walk from one corner of a basket-ball
court to its oppposite corner along its
sides.
? Measure the distance covered by you
and magnitude of the displacement.
? What difference would you notice
between the two in this case?
Activity ______________8.4
? Automobiles are fitted with a device
that shows the distance travelled. Such
a device is known as an odometer. A
car is driven from Bhubaneshwar to
New Delhi. The difference between the
final reading and the initial reading of
the odometer is 1850 km.
? Find the magnitude of the displacement
between Bhubaneshwar and New Delhi
by using the Road Map of India.
The total path length covered by the object
is OA + AC, that is 60 km + 35 km = 95 km.
This is the distance covered by the object. To
describe distance we need to specify only the
numerical value and not the direction of
motion. There are certain quantities which
are described by specifying only their
numerical values. The numerical value of a
physical quantity is its magnitude. From this
example, can you find out the distance of the
final position C of the object from the initial
position O? This difference will give you the
numerical value of the displacement of the
object from O to C through A. The shortest
distance measured from the initial to the final
position of an object is known as the
displacement.
Can the magnitude of the displacement
be equal to the distance travelled by an
object? Consider the example given in
(Fig. 8.1). For motion of the object from O to
A,  the distance covered is 60 km  and the
magnitude of displacement is also 60 km.
During its motion from O to A and back to B,
the distance covered = 60 km + 25 km = 85 km
Fig. 8.1: Positions of an object on a straight line path
while the magnitude of displacement = 35 km.
Thus, the magnitude of displacement (35 km)
is not equal to the path length (85 km).
Further, we will notice that the magnitude of
the displacement for a course of motion may
be zero but the corresponding distance
covered is not zero. If we consider the object
to travel back to O, the final position concides
with the initial position, and therefore, the
displacement is zero. However, the distance
covered in this journey is OA + AO = 60 km +
60 km = 120 km. Thus, two different physical
quantities — the distance and the
MOTION 99 SCIENCE 100
uestions
1. An object has moved through a
distance. Can it have zero
displacement? If yes, support
your answer with an example.
2. A farmer moves along the
boundary of a square field of side
10 m in 40 s. What will be the
magnitude of displacement of the
farmer at the end of 2 minutes
20 seconds?
3. Which of the following is true for
displacement?
(a) It cannot be zero.
(b) Its magnitude is greater than
the distance travelled by the
object.
8.1.2 UNIFORM MOTION AND NON-
UNIFORM MOTION
Consider an object moving along a straight
line. Let it travel 50 km in the first hour,
50 km more in the second hour, 50 km in the
third hour and 50 km in the fourth hour. In
this case, the object covers 50 km in each
hour. As the object covers equal distances in
equal intervals of time, it is said to be in
uniform motion.  The time interval in this
motion may be small or big. In our
day-to-day life, we come across motions where
objects cover unequal distances in equal
intervals of time, for example, when a car is
moving on a crowded street or a person is
jogging in a park. These are some instances
of non-uniform motion.
Activity ______________8.5
? The data regarding the motion of two
different objects A and B are given in
Table 8.1.
? Examine them carefully and state
whether the motion of the objects is
uniform or non-uniform.
Q
(a)
(b)
Fig. 8.2
Table 8.1
Time Distance Distance
travelled by travelled by
object A in m object  B in m
9:30 am 10 12
9:45 am 20 19
10:00 am 30 23
10:15 am 40 35
10:30 am 50 37
10:45 am 60 41
11:00 am 70 44
8.2 Measuring the Rate of Motion
MOTION 101
Look at the situations given in Fig. 8.2. If
the bowling speed is 143 km h
–1 
in Fig. 8.2(a)
what does it mean? What do you understand
from the signboard in Fig. 8.2(b)?
Different objects may take different
amounts of time to cover a given distance.
Some of them move fast and some move
slowly. The rate at which objects move can
be different. Also, different objects can move
at the same rate. One of the ways of
measuring the rate of motion of an object is
to find out the distance travelled by the object
in unit time. This quantity is referred to as
speed. The SI unit of speed is metre per
second. This is represented by the symbol
m s
–1 
or m/s.
 
The other units of speed include
centimetre per second (cm s
–1
) and kilometre
per hour (km h
–1
). To specify the speed of an
object, we require only its magnitude. The
speed of an object need not be constant. In
most cases, objects will be in non-uniform
motion. Therefore, we describe the rate of
motion of such objects in terms of their
average speed. The average speed of an object
is obtained by dividing the total distance
travelled by the total time taken. That is,
average speed = 
Total distance travelled
Total time taken
If an object travels a distance s in time t then
its speed v is,
v = 
s
t
(8.1)
Let us understand this by an example. A
car travels a distance of 100 km in 2 h. Its
average speed is 50 km h
–1
. The car might
not have travelled at 50 km h
–1
 all the time.
Sometimes it might have travelled faster and
sometimes slower than this.
Example 8.1 An object travels 16 m in 4 s
and then another 16 m in 2 s. What is
the average speed of the object?
Solution:
Total distance travelled by the object =
16 m + 16 m = 32 m
Total time taken = 4 s + 2 s = 6 s
Average speed = 
Total distance travelled
Total time taken
= 
32 m
6s
= 5.33 m s
–1
Therefore, the average speed of the object
is 5.33 m s
–1
.
8.2.1 SPEED WITH DIRECTION
The rate of motion of an object can be more
comprehensive if we specify its direction of
motion along with its speed. The quantity that
specifies both these aspects is called velocity.
Velocity is the speed of an object moving in a
definite direction. The velocity of an object
can be uniform or variable. It can be changed
by changing the object’s speed, direction of
motion or both. When an object is moving
along a straight line at a variable speed, we
can express the magnitude of its rate of
motion in terms of average velocity. It is
calculated in the same way as we calculate
average speed.
In case the velocity of the object is
changing at a uniform rate, then average
velocity is given by the arithmetic mean of
initial velocity and final velocity for a given
period of time. That is,
average velocity = 
initial velocity +finalvelocity
2
Mathematically, v
av
  = 
u+v
2
(8.2)
where v
av
 is the average velocity, u is the initial
velocity and v is the final velocity of the object.
Speed and velocity have the same units,
that is, m s
–1
 or m/s.
Activity ______________8.6
? Measure the time it takes you to walk
from your house to your bus stop or
the school. If you consider that your
average walking speed is 4 km h
–1
,
estimate the distance of the bus stop
or school from your house.
Page 5


In everyday life, we see some objects at rest
and others in motion. Birds fly, fish swim,
blood flows through veins and arteries and
cars move. Atoms, molecules, planets, stars
and galaxies are all in motion. We often
perceive an object to be in motion when its
position changes with time. However, there
are situations where the motion is inferred
through indirect evidences. For example, we
infer the motion of air by observing the
movement of dust and the movement of leaves
and branches of trees. What causes the
phenomena of sunrise, sunset and changing
of seasons? Is it due to the motion of the
earth? If it is true, why don’t we directly
perceive the motion of the earth?
An object may appear to be moving for
one person and stationary for some other. For
the passengers in a moving bus, the roadside
trees appear to be moving backwards. A
person standing on the road–side perceives
the bus alongwith the passengers as moving.
However, a passenger inside the bus sees his
fellow passengers to be at rest. What do these
observations indicate?
Most motions are complex. Some objects
may move in a straight line, others may take
a circular path. Some may rotate and a few
others may vibrate. There may be situations
involving a combination of these. In this
chapter, we shall first learn to describe the
motion of objects along a straight line. We
shall also learn to express such  motions
through simple equations and graphs. Later,
we shall discuss ways of describing circular
motion.
Activity ______________8.1
? Discuss whether the walls of your
classroom are at rest or in motion.
Activity ______________8.2
? Have you ever experienced that the
train in which you are sitting appears
to move while it is at rest?
? Discuss and share your experience.
Think and Act
We sometimes are endangered by the
motion of objects around us, especially
if that motion is erratic and
uncontrolled as observed in a flooded
river , a hurricane or a tsunami. On the
other hand, controlled motion can be a
service to human beings such as in the
generation of hydro-electric power. Do
you feel the necessity to study the
erratic motion of some objects and
learn to control them?
8.1 Describing Motion
We describe the location of an object by
specifying a reference point. Let us
understand this by an example. Let us
assume that a school in a village is 2 km north
of the railway station. We have specified the
position of the school with respect to the
railway station. In this example, the railway
station is the reference point. We could have
also chosen other reference points according
to our convenience. Therefore, to describe the
position of an object we need to specify a
reference point called the origin.
8 8
8 8 8
M M M M MOTION OTION OTION OTION OTION
Chapter
8.1.1 MOTION ALONG A STRAIGHT LINE
The simplest type of motion is the motion
along a straight line. We shall first learn to
describe this by an example. Consider the
motion of an object moving along a straight
path. The object starts its journey from O
which is treated as its reference point
(Fig. 8.1). Let A, B and C represent the
position of the object at different instants. At
first, the object moves through C and B and
reaches A. Then it moves back along the same
path and reaches C through B.
displacement, are used to describe the overall
motion of an object and to locate its final
position with reference to its initial position
at a given time.
Activity ______________8.3
? Take a metre scale and a long rope.
? Walk from one corner of a basket-ball
court to its oppposite corner along its
sides.
? Measure the distance covered by you
and magnitude of the displacement.
? What difference would you notice
between the two in this case?
Activity ______________8.4
? Automobiles are fitted with a device
that shows the distance travelled. Such
a device is known as an odometer. A
car is driven from Bhubaneshwar to
New Delhi. The difference between the
final reading and the initial reading of
the odometer is 1850 km.
? Find the magnitude of the displacement
between Bhubaneshwar and New Delhi
by using the Road Map of India.
The total path length covered by the object
is OA + AC, that is 60 km + 35 km = 95 km.
This is the distance covered by the object. To
describe distance we need to specify only the
numerical value and not the direction of
motion. There are certain quantities which
are described by specifying only their
numerical values. The numerical value of a
physical quantity is its magnitude. From this
example, can you find out the distance of the
final position C of the object from the initial
position O? This difference will give you the
numerical value of the displacement of the
object from O to C through A. The shortest
distance measured from the initial to the final
position of an object is known as the
displacement.
Can the magnitude of the displacement
be equal to the distance travelled by an
object? Consider the example given in
(Fig. 8.1). For motion of the object from O to
A,  the distance covered is 60 km  and the
magnitude of displacement is also 60 km.
During its motion from O to A and back to B,
the distance covered = 60 km + 25 km = 85 km
Fig. 8.1: Positions of an object on a straight line path
while the magnitude of displacement = 35 km.
Thus, the magnitude of displacement (35 km)
is not equal to the path length (85 km).
Further, we will notice that the magnitude of
the displacement for a course of motion may
be zero but the corresponding distance
covered is not zero. If we consider the object
to travel back to O, the final position concides
with the initial position, and therefore, the
displacement is zero. However, the distance
covered in this journey is OA + AO = 60 km +
60 km = 120 km. Thus, two different physical
quantities — the distance and the
MOTION 99 SCIENCE 100
uestions
1. An object has moved through a
distance. Can it have zero
displacement? If yes, support
your answer with an example.
2. A farmer moves along the
boundary of a square field of side
10 m in 40 s. What will be the
magnitude of displacement of the
farmer at the end of 2 minutes
20 seconds?
3. Which of the following is true for
displacement?
(a) It cannot be zero.
(b) Its magnitude is greater than
the distance travelled by the
object.
8.1.2 UNIFORM MOTION AND NON-
UNIFORM MOTION
Consider an object moving along a straight
line. Let it travel 50 km in the first hour,
50 km more in the second hour, 50 km in the
third hour and 50 km in the fourth hour. In
this case, the object covers 50 km in each
hour. As the object covers equal distances in
equal intervals of time, it is said to be in
uniform motion.  The time interval in this
motion may be small or big. In our
day-to-day life, we come across motions where
objects cover unequal distances in equal
intervals of time, for example, when a car is
moving on a crowded street or a person is
jogging in a park. These are some instances
of non-uniform motion.
Activity ______________8.5
? The data regarding the motion of two
different objects A and B are given in
Table 8.1.
? Examine them carefully and state
whether the motion of the objects is
uniform or non-uniform.
Q
(a)
(b)
Fig. 8.2
Table 8.1
Time Distance Distance
travelled by travelled by
object A in m object  B in m
9:30 am 10 12
9:45 am 20 19
10:00 am 30 23
10:15 am 40 35
10:30 am 50 37
10:45 am 60 41
11:00 am 70 44
8.2 Measuring the Rate of Motion
MOTION 101
Look at the situations given in Fig. 8.2. If
the bowling speed is 143 km h
–1 
in Fig. 8.2(a)
what does it mean? What do you understand
from the signboard in Fig. 8.2(b)?
Different objects may take different
amounts of time to cover a given distance.
Some of them move fast and some move
slowly. The rate at which objects move can
be different. Also, different objects can move
at the same rate. One of the ways of
measuring the rate of motion of an object is
to find out the distance travelled by the object
in unit time. This quantity is referred to as
speed. The SI unit of speed is metre per
second. This is represented by the symbol
m s
–1 
or m/s.
 
The other units of speed include
centimetre per second (cm s
–1
) and kilometre
per hour (km h
–1
). To specify the speed of an
object, we require only its magnitude. The
speed of an object need not be constant. In
most cases, objects will be in non-uniform
motion. Therefore, we describe the rate of
motion of such objects in terms of their
average speed. The average speed of an object
is obtained by dividing the total distance
travelled by the total time taken. That is,
average speed = 
Total distance travelled
Total time taken
If an object travels a distance s in time t then
its speed v is,
v = 
s
t
(8.1)
Let us understand this by an example. A
car travels a distance of 100 km in 2 h. Its
average speed is 50 km h
–1
. The car might
not have travelled at 50 km h
–1
 all the time.
Sometimes it might have travelled faster and
sometimes slower than this.
Example 8.1 An object travels 16 m in 4 s
and then another 16 m in 2 s. What is
the average speed of the object?
Solution:
Total distance travelled by the object =
16 m + 16 m = 32 m
Total time taken = 4 s + 2 s = 6 s
Average speed = 
Total distance travelled
Total time taken
= 
32 m
6s
= 5.33 m s
–1
Therefore, the average speed of the object
is 5.33 m s
–1
.
8.2.1 SPEED WITH DIRECTION
The rate of motion of an object can be more
comprehensive if we specify its direction of
motion along with its speed. The quantity that
specifies both these aspects is called velocity.
Velocity is the speed of an object moving in a
definite direction. The velocity of an object
can be uniform or variable. It can be changed
by changing the object’s speed, direction of
motion or both. When an object is moving
along a straight line at a variable speed, we
can express the magnitude of its rate of
motion in terms of average velocity. It is
calculated in the same way as we calculate
average speed.
In case the velocity of the object is
changing at a uniform rate, then average
velocity is given by the arithmetic mean of
initial velocity and final velocity for a given
period of time. That is,
average velocity = 
initial velocity +finalvelocity
2
Mathematically, v
av
  = 
u+v
2
(8.2)
where v
av
 is the average velocity, u is the initial
velocity and v is the final velocity of the object.
Speed and velocity have the same units,
that is, m s
–1
 or m/s.
Activity ______________8.6
? Measure the time it takes you to walk
from your house to your bus stop or
the school. If you consider that your
average walking speed is 4 km h
–1
,
estimate the distance of the bus stop
or school from your house.
SCIENCE 102
= 
50
km 1000m 1h
××
h 1km 3600s
= 13.9 m s
–1
The average speed of the car is
50 km h
–1
 or 13.9 m s
–1
.
Example 8.3 Usha swims in a 90 m long
pool. She covers 180 m in one minute
by swimming from one end to the other
and back along the same straight path.
Find the average speed and average
velocity of Usha.
Solution:
Total distance covered by Usha in 1 min
is 180 m.
Displacement of Usha in 1 min = 0 m
Average speed = 
Total distance covered
Totaltimetaken
=
180m 180 m 1 min
=×
1min 1min 60s
= 3 m s
-1
Average velocity = 
Displacement
Totaltimetaken
= 
0m
60 s
= 0 m s
–1
The average speed of Usha is 3 m s
–1
and her average velocity is 0 m s
–1
.
8.3 Rate of Change of Velocity
During uniform motion of an object along a
straight line,  the velocity remains constant
with time. In this case, the change in velocity
of the object for any time interval is zero.
However, in non-uniform motion, velocity
varies with time. It has different values at
different instants and at different points of
the path. Thus, the change in velocity of the
object during any time interval is not zero.
Can we now express the change in velocity of
an object?
Activity ______________8.7
? At a time when it is cloudy, there may
be frequent thunder and lightning. The
sound of thunder takes some time to
reach you after you see the lightning.
? Can you answer why this happens?
? Measure this time interval using a
digital wrist watch or a stop watch.
? Calculate the distance of the nearest
point of lightning. (Speed of sound in
air = 346 m s
-1
.)
uestions
1. Distinguish between speed and
velocity.
2. Under what condition(s) is the
magnitude of average velocity of
an object equal to its average
speed?
3. What does the odometer of an
automobile measure?
4. What does the path of an object
look like when it is in uniform
motion?
5. During an experiment, a signal
from a spaceship reached the
ground station in five minutes.
What was the distance of the
spaceship from the ground
station? The signal travels at the
speed of light, that is, 3 × 10
8
m s
–1
.
Example 8.2 The odometer of a car reads
2000 km at the start of a trip and
2400 km at the end of the trip. If the
trip took 8 h, calculate the average
speed of the car in km h
–1
 and m s
–1
.
Solution:
Distance covered by the car,
s = 2400 km – 2000 km = 400 km
Time elapsed, t = 8 h
Average speed of the car is,
v
av
 =  
400 km
8h
=
s
t
= 50 km h
–1
Q