3. POSITION
a b c d
• Suppose four a,b,c,d are seating in a
row equidistant from their neighbors
from left to right as shown
• Position of b with respect to
• a is immediate right
• c is immediate left
• d is second to the left
• Thus position is relative which varies
according to the reference point.
Left to right
4. Relative and Absolute Position
In the figure position of B with respect to A is AB in
East
Respect to C is CB North East.
• Thus position of a particular point can vary with
different points
• This is known as Relative Position .
• But in order to consider all points in one frame we
need to consider one point as a absolute referral
point an position of all other points with respect to
that point will be their
Absolute Position.
For example consider O as a absolute point then
position of all other points with respect to O will be
their absolute position for B is OB in North East.
Similarly A is OA North West and So On.
A B
North
south
East
west
C D
O
Note :- 1. We Can take any point as absolute according to our convenience.
2. Direction as well as distance both is required to know ones position.
5. Illustrative Problem
• Questions:
1. What is the position of E with respect to D?
2. What is the position of O with respect to B?
3. What is the position of B with respect to E?
4. Find the absolute position of all points Considering O as absolute
point?
5. Find the absolute position of all points considering A as absolute
Point?
A B
o
3m
4m
3m
4m
D
E
North
South
East
West
6. .Concept of Rest and Motion
• Rest : A body is said to be in rest if its position does not vary with respect
to a given referral point as time passes.
• Motion: A body is said to be in motion if there is a continues change in its
position with respect to a given referral as time passes.
• Concept of rest and motion is related to referral change in position so a
single object can be at rest or motion same time with different referral
points.
• If we consider a single object as referral point and consider it as rest, as a
absolute point any object which is at rest with respect to that point is
considered at rest and same case with motion.
• In general we consider Earth as absolute point considering it at rest,
Although It is in motion with respect to Sun and other planets
7.
8. SCALER AND VECTOR
l
l
l
AB is a line segment of
length l. AB has no
specified direction.
AB is a Scalar with
magnitude l
Also AB=BA
BA is a directed line
segment directed from B to
A. The length of BA is l that
is its magnitude is l. Thus
BA is a vector
AB is a directed line
segment directed from A to
B. The length of AB is l that
is its magnitude is l. Thus
AB is a vector
Note :- Vector BA is not equal to Vector AB as their directions are
different although they are equal in magnitude. For two vectors to be
equal both direction and magnitude should be equal.
Since the both vectors are equal in magnitude but just opposite in
directions. We can write vectorAB= -VectorBA
9. Distance And Displacement
Distance Displacement
The actual path covered during motion of
a body
The Change in position made during
motion of a body is known as
displacement
It is needed not to be the Shortest path
between two points
It is the shortest path between initial and
final position
It is the Scaler quantity as It does not
have any particular direction
It is a vector quantity as it is always
directed.
10. Illustrative Examples: A
B c
In the figure there can be various paths, but the
shortest path denotes actual change in position from
Initial point A to final point B which we call as
displacement.
11. Illustrative Example:
A B
x= 𝜋𝑟
𝑑 = 2𝑟
C
If path taken between A and B
is through arc it is
Displacement is
Suppose a boy running on the track , he starts from A and after completing one round his
distance is 2𝜋r
But his position remains same thus displacement is zero.
12. Concept of Rate:
.Rate is defined as ratio of change in two quantities
.Rate is of two types :-
.Average Rate of quantity A with respect to B
net change in Anet change in B
.Instantaneous Rate is rate at an Instant that is for very short interval of
time.
.Speed, Velocity and Acceleration are examples of Rate.
13. Speed and Velocity
• Average speed = total distance travelled/total time taken
• Instant speed = speed during a very small interval of time
• Average Velocity= Net Displacement /total time taken
• Instant velocity= velocity during a very small interval of time
• Velocity is related to displacement and thus is a vector quantity.
14. Acceleration
• Acceleration = Rate of change of velocity with respect to time
• Same as velocity there is a concept of Instant and average
acceleration
• Acceleration is a vector quantity.
• Acceleration is related to change in velocity. Therefor change of
velocity in terms of magnitude or direction both can be regarded as
accelerated motion.
In this case, the direction of velocity is keep on
changing, but the magnitude is constant. Such kind of
motion is also an example of accelerated motion.
15. Uses of Graphs:
Y
X
o
Y’
X’
Y +ve
X +ve
Y +ve
X -ve
Y -ve
X -ve
Y -ve
X +ve
A Graph is a pictorial representation which denotes relation between two
quantities.
In general we take X axis as Independent quantity for example we take time as X
axis as time is keep on going at its own rate independent of any other factor.
16. Concept of Slope in Graph:
• Slope of any graph represents its rate.
Linear Graph: constant Rate
o
Y
X
Ax+By+C=0
Y=(-C-Ax)/B= -C/B-Ax/B= Mx+c
Here M is the slope of Graph M=-A/B and c is Y Intercept.
This is the graph of linear Equation in which we represent how y
varies with respect to x. Thus slope is constant.
(0,c)
y2
y1
x2
x1
y2-y1
X2-x1
In this case slope M=(y2-y1)/(x2-x1)
which is constant through out.
Considering distance as Y axis and time
as X axis we came to know slope is
speed. M represents Average Speed
between two points.
17. A
B
C
distance
time
𝜃1
𝜃2
𝜃3
In this diagram, motion of three objects A,B and C is shown.
We can see they have different speeds
The speed is slope of graph which is represented by angle made
By graph on time axis.
Slope =tan 𝜃
Roughly in this case we can say since
Speed of c is greater than B which is greater than of A
𝜃3 > 𝜃2 > 𝜃1
18. NON LINEAR GRAPH: When
Rate is not constant
Average and instantaneous Speed:
Distance
time
A
B
C
D
∆t
s
𝜃1
𝜃2
𝜃3
∆
𝜃1 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑖𝑛𝑠𝑡𝑎𝑛𝑡 𝑠𝑝𝑒𝑒𝑑 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝐴
𝜃2 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑖𝑛𝑠𝑡𝑎𝑛𝑡 𝑠𝑝𝑒𝑒𝑑 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝐵
𝜃3 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 𝑑𝑢𝑟𝑖𝑛𝑔
Its motion from A to C
tan 𝜃3 = ∆𝑠/∆𝑡=average speed A and C
tan 𝜃2 = 𝑠𝑝𝑒𝑒𝑑 𝑎𝑡 𝐵
tan 𝜃1 = 𝑠𝑝𝑒𝑒𝑑 𝑎𝑡 𝐴
19. Distance Time Graph:
• Considering Motion in Straight Line:
Situation 1:
A person moving from his house consider it point A. He travels in a straight road for 5 second
with a constant Speed of 1m/s for 4seconds and reaches B. He stops their for 5 second and again
started moving in same direction for 4 seconds and reaches point C.
A B C
4m 4m
Graph showing Distance Time Relation according to situation 1
Note:
• In this case
• Total distance travelled = 8m
• Total time taken= 12second
• Average speed= total distance/total time
= 8m/12sec=0.67m/sec
• Total position displaced=total displacement=8m
• Average velocity=0.67m/sec from A to C
20. Position Time Graph:
• Situation 2:
Consider an object is moving in
straight direction. It starts from
origin moves first 3m in a
direction for 1second. Then
take pause for 1 second, then
moves 4m in same direction for
2 seconds, then it rests for 2
seconds, then moves backward
direction 4 m in 1 second.
A B C
3m 4m
0
1
2
3
4
5
6
7
8
0 2 4 6 8
Position(m)
Time(s)
22. Velocity Time Graph:
• Velocity time graph represents how velocity will vary in accordance with time.
• Slope of velocity time graph represents acceleration.
• Area under velocity time graph represents distance and displacement.
• If we consider distance we add all areas under curve, in displacement we subtract
those areas that is below time graph.
• Distance = A+B Displacement = A-B
A
B
𝜃1 𝜃2
X
Y
𝜃1 𝑎𝑛𝑑 𝜃2 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝑋
And Y respectively.
𝜃3
𝜃3 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑎𝑣𝑒𝑟𝑎𝑔𝑒
Acceleration between x and y
velocity
time
23. UNIFORM AND NON UNIFORM MOTION:
• Uniform motion: Equal distance travelled at equal interval of time
• Non Uniform motion: Unequal distance at unequal interval of time
Uniform Motion
Non Uniform Motion
distance
time
distance distance
time
time
24. UNIFORMALY ACCELERATED MOTION:
• It is the motion with constant
acceleration
• Such motions are governed
by three equations of motion
which can be proved using
velocity time graph.
