The document discusses various concepts related to motion including: 1) Motion is defined as a change in position of an object over time relative to a reference point. 2) Examples of motion include swings, merry-go-rounds, pendulums, and watch hands. 3) Distance traveled refers to the actual path length, while displacement is the straight line distance between start and end points. 4) Speed, velocity, acceleration, and other concepts are introduced along with relevant equations. Uniform and non-uniform variations of each concept are also discussed.

1. Science
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2. MOTION
 Motion:
A body is said to be in motion
when its position changes continuously
with respect to a stationary object taken as
a reference point.
 Characteristic of Motion :
A common
characteristic of all moving object are they
change their position with respect to time.

3.  Examples of motion:
1. Swing
2. Merry go round
3. Pendulum of a clock
4. Hands of a watch

4.  If a body moves fairly fast, then its
movement can be observed easily. But
if a body moves very slowly, then it
become difficult to observe its
movement immediately.
 For example:
A watch had three hands
i.e. a second’s, minute’s & hour’s. The
speed of second’s is fast so, its motion
can be observed. But the minute’s &
hour’s hand is slow so, its motion
cannot be observed.

5.  Distance travelled:
The distance
travelled b a body is the actual
length of the path covered by a
moving body irrespective of the
direction in which the body travels.
It is a scalar quantity.

6.  When a body moves from one point
to another, the distance travelled
refers to the actual length of the
indirect path whereas displacement
refers to the straight line path
between the initial & the final
positions.
 Displacement:
The shortest distance
between the initial position & the final
position is known as its
displacement.
It is a vector quantity.

7.  Scalar quantity:
A physical quantity
having only magnitude is known as a
scalar quantity. A scalar quantity has
no direction.
 Vector quantity:
A physical quantity
having only magnitude as well as
direction is known as vector quantity.

8.  The distance travelled by a moving
body can't be zero but the final
displacement of a moving body can
be zero.
 Uniform Motion:
A body has a uniform
motion if it travels equal distances in
equal intervals of time.

9. GRAPH OF UNIFORM MOTION

10.  Non–Uniform Motion:
A body has a
non–uniform motion if it travels equal
distances in equal intervals. of time.

11.  Non-uniform motion is also called
accelerated motion.
 Speed:
Speed of a body is the distance
travelled by it per unit time.
Formula for speed is:
Speed = Distance travelled
Time taken
Where:
v = speed
s = distance travelled
and t = time taken

12.  Speed gives the idea how slow or fast the
body is moving.
 The SI unit of speed is meters per second.
 The small values of speed are expressed in
the unit of cm. per sec. To express high
speed values we use the unit of km. per hr.
 It is a scalar quantity because it has only
magnitude not specified direction.
 If we have to compare the speeds of a
number of bodies, then we must express
the speed of all of them in the same unit.

13.  Average speed:
The average sped of a
body is the total distance travelled by the
total time taken to cover this distance.
Formula for Average speed is:
Average speed = Total distance travelled
Total time taken
Where:
v = average speed
s = total distance travelled
and t = total time taken

14.  Speedometer:
An instrument for
measuring speed of the moving
vehicle.
 Odometer:
An instrument for
measuring distance travelled by the
vehicle.

15.  Uniform speed:
A body has a uniform
speed if it travels equal distances in
equal intervals of time.
 Velocity:
Velocity of a body is the
distance travelled by it per unit time in
a given direction.
Formula for Velocity is:
Velocity= Displacement
Time taken

16. v = s
t
Where:
v = velocity
s = displacement
and t = time taken
 The SI unit of velocity is meter per second.
 It is a vector quantity because is has
magnitude as well as direction.
 The direction of velocity is the same as the
direction of displacement of body.

17.  Uniform velocity:
A body has uniform
velocity if it travels in a specified direction
in a straight line and moves over equal
distances in equal intervals of time, no
matter how small how these time intervals
may be.
The velocity of a body can be changed
in two ways:
(i) By changing the speed of the body, and
(ii) By keeping the speed constant but by
changing the direction.

18.  Speed and Velocity are not always
equal in magnitude.
 The magnitude of speed and velocity of
a moving body is equal only if the body
moves in a single straight line. If,
however a body does not move in a
single straight line, then the speed &
velocity of the body is not equal.
 The average speed of a moving can
never be zero, but the average velocity
of a moving body can be zero.

19.  Acceleration:
Acceleration of a body is
defined as the rate of change in velocity
with time.
Formula for Acceleration is:
Acceleration = Final velocity – Initial velocity
Time taken
a = v-u
t

20. Where, a = acceleration of the body
v = final velocity of the body
u = initial velocity of the body
and t = time taken for the
change in velocity
 The SI unit of acceleration is “meter
per second square.”
 Acceleration is a vector quantity
because it has magnitude as well as
direction.

21.  Uniform Acceleration:
A body has a
uniform acceleration if the velocity
changes at a uniform rate.
 Example of Uniform Acceleration:
i. The motion of a freely falling body.
ii. The motion of a bicycle going down
the slope of a road when the rider is
not pedaling and wind is negligible.
iii. The motion of a ball rolling down an
inclined plane.

22.  The velocity-time graph of a body
having uniformly accelerated motion is
a straight line.
 Non-Uniform Acceleration:
A body has
a non-uniform acceleration if its
velocity changes at a non-uniform rate.
 Retardation:
It is the negative of
acceleration.

23. GRAPHOF RETARDATION

24. GRAPH OF NON-UNIFORM
ACCELERATION

25.  If the velocity of a body increases the
acceleration is positive and if the
velocity decreases the acceleration is
negative.
Formula for Retardation is:
Retardation = Final velocity – Initial velocity
Time taken
 SI unit of retardation is meter per
second square.
 Retardation is actually acceleration
with negative sign.

26.  Average Velocity:
If the object is
changing at uniform rate, then average
velocity is given by the arithmetic mean
of initial velocity & final velocity for a
given period of time.
Formula for average velocity:
Average velocity = Initial velocity+ Final velocity
2

27.  Derivation of Formula for Equation
of Motion:
 Equation 1- V = u+at

28.  Consider a velocity time graph for a
body moving under uniform
acceleration ‘a’
Initial velocity u ≠ o
In the v-t graph
OA = DC = u (initial velocity)
EO = BC = v (final velocity)
AD = OC = t (time taken)
BD = BC - DC
= v - u

29. The slope of v-t graph gives the
acceleration of the object.
acceleration ‘a’
a = BD = (v-u)
AD t
or v-u = at
or v = u+at

30.  Equation 2- S= ut + ½ at^2

31. v-t graph
Let the body travels distance ‘s’ in time ‘t’
under uniform acceleration ‘a’.
Distance travelled (s) = area enclosed under
the velocity time graph.
S = area of triangle ABD
+ area of rectangle OADC
= ½  AD BD AO OC
= AD = OC = t
BD = EA =(v-u)
AO = DC = u

32. OC = AD = t
= ½  t  (v-u)  ut
= ut  ½ (v-u) t : Equation 1
We know that
v u  at
 v  u  at : Equation 2
Putting the value of
v  u  at in Equation 1
We get,
s  ut + ½ (at) t
s  ut  ½ at²

33. Equation 3- v²  u²  2as

34. v-t graph
Let the body travels distance ‘s’ in time ‘t’
under uniform acceleration ‘a’.
Distance travelled (s) = area enclosed under
the velocity time graph.

35. In the trapezium OABC
Area  ½ (sum of parallel side) height
 ½  OC (OA  CB)
Distance travelled (s)
s  ½  t (u  v)
We know that v  u  at
t  v  u
a
s  ½  v  u v  u
a

36.  Circular Motion:
When a body moves in
a circle, it is called circular motion.
 When a body moves along a circular
path, then its direction of motion keeps
changing continuously.
 Uniform Circular Motion:
When a body
moves in circular path with uniform
speed, its motion is called uniform
circular motion.

37. s  v²  u²
2a
v²  u²  2as
or v²  u²  2as

38.  The force is needed to produce circular
motion.
 Centripetal Force:
The force which is
needed to make an object travel in a
circular path is called centripetal force.
 Example of Uniform Circular Motion:
i. Artificial satellite move in a circular
motion around the earth.
ii. The moon moves around the earth.
iii. The earth moves around the sun.

39. iv. A athlete moving on a circular path
with a constant speed.
v. The tip of a second’s hand of a watch.
 To Calculate the Speed of a Body in
Uniform Circular Motion:
v  2  22  r
7  t

40. SUMITTED TO
MR KHANKRIAL SIR
SUMITTED FROM
BISHMAY
IX ‘C’