A
vector quality is represented by an arrow over the symbol of the physical
quantity. For
example,
A or A , where A represents, the magnitude of the vector quantity A.
Sometimes
bold A instead of A is used to represent a vector and an ordinary A
to
represent
its magnitude. The vector quantities in the table 2.1 are represented by bold
letter.
In
figure, a vector quantity represented by an arrow headed
straight line. The length of the straight line represents
the magnitude and the arrow head
indicates
the direction of the vector. For example, in
figure
2.2 displacement of 50km has been
represented
by 1cm. Hence the vector A in this
figure,
whose length is 3cm represents a
displacement
of 150km towards west. The vector B
represents
a displacement of 100km towards north at
an
angle of 300 with
the east.
2.4 Different quantities related
to motion
Distance and Displacement:
Suppose,
Ovi ran 100m from his school gate. It is true that
Ovi
is 100m away from the gate, but it does not tell the
exact
position of Ovi. Because Ovi can be 100m away to
the
east, to the west, to the north, to the south or any other
directions.
To know exactly the change of position of Ovi,
the
direction towards which he moved 100m should also be
known.
If it is stated that Ovi ran 100m from the gate to the
east
then his exact position will be known definitely. If you
go
straight to the east from the gate you will find Ovi at a
distance
of 100m. The physical quantity which was first
used
to indicate the change of position of Ovi is distance. This is a scalar
quantity. In the
second
case, direction has also been mentioned along with distance, this is called
displacement.
This is a vector quantity. Change of position or distance in a definite
direction
is displacement. So, the change of position of an object with respect to its
surrounding
in a definite direction is called displacement.
The
minimum distance, that is, the linear distance between the initial and final
position
of
a body is the magnitude of its displacement at its direction is towards final
position
from
the initial position.
The
displacement does not depend on the path of the object. An object can move from
position
A to position B following different paths. But its displacement will be from A
Fig-2.2
Fig-2.3
W
E
S
N
32
Physics
towards
B. The minimum distance between A and B, that is, in this case the linear
distance
AB is the magnitude of displacements. AB and its direction is towards B from
A.
Here, it is a vector quantity, since displacement has both magnitude and
direction.
The
dimension of displacement is the same as that of distance.
Therefore,
[ s ] = L
The
unit of displacement is the same as that of distance that is meter (m). The
displacement
of a body is 50m towards north means that the body has moved 50m from
its
initial position towards north direction.
Speed : Suppose in the previous example, Ovi takes 50 seconds, to
travel 100m
distance.
If Mitu covers the same distance in 40 seconds, who goes faster ? Ovi or Mitu,
definitely
Mitu goes faster because she takes less time.
Suppose,
Ovi travels 100m in 50 seconds, Mitu travels 75m in 30 seconds can we say
Ovi
goes slower than Mitu ? Does not Ovi travel more distance than Mitu ? The
distance
of
a particular time Ovi and Mitu travels has to be compared to know who goes
faster.
Let
the particular time be 1 second therefore,
In
1 second Ovi travels
50
= 2 meter
In
1 second Mitu travels
75
30
= 2.5 meter
So,
Mitu goes faster than Ovi because in 1 second Mitu travels more distance than
Ovi.
From
the above discussion we can understand time and distance determines who goes
faster.
The
quantity by which we can measure how fast a body moves or distance traveled, is
called
speed. Speed expresses the rate of change position of a body. The rate of
change
of
position of a body with time is called the speed.
Speed
of a body is measured by the distance traveled per unit time. i.e
Speed
=
distance
time
If
a moving body travels a distance `d’ in time `t’ then the speed v is
The
direction of rate of change of position of the body cannot be known by the
speed. So
it has no direction. Therefore, speed is a
scalar quantity.
