The document discusses types of motion, including uniform and non-uniform motion, speed, velocity, and acceleration. It explains the laws of motion, the principle of conservation of momentum, and provides graphical representations of motion such as distance-time and velocity-time graphs. Additionally, it touches on different types of motion including linear, rotatory, and circular motion.

3. Motion

4. Uniform Motion:
When an object covers equal distance in equal interval of time,
the motion is called uniform motion. For example – if a moving
vehicle covers a distance of 10 km every hour, the motion of the
vehicle is called uniform motion.
Non-Uniform Motion:
When an object covers unequal distance in equal interval of
time, the motion is called non-uniform motion. For example – If
moving vehicle covers a distance of 10 km in the first hour,
covers a distance of 20 km in the second hour, covers a distance
of 5 km in the third hour, etc. the motion of the vehicle is called
non-uniform motion.

5. Speed
• Distance covered by a moving object in unit time is called distance.
• Where, v = speed, s = distance, t = total time.
• SI unit of speed is meter per second (m/s).

6. Average speed
• The average distance covered in unit time by a moving object is called average speed.
Average speed is the ratio of total distance covered and total time taken.
• Where, v = Average Speed, s = Total distance covered, t = total time taken.
• SI unit of average speed is meter per second (m/s).

7. Velocity
• The speed of a moving object in particular direction is
called velocity. Velocity has both magnitude and direction
while speed has only magnitude and no direction.
• Velocity of an object is the distance covered in particular
direction in unit time.

8. Average Velocity
The arithmetic mean of velocity of an object moving along a straight line is called the average
velocity.
The displacement of a moving object in unit time is also called the average velocity.

9. Acceleration
• The rate of change in velocity is called acceleration. Acceleration is generally denoted by
‘a’ or f.
• Where, ‘a’ is acceleration, ‘v’ is final velocity, ‘u’ is initial velocity and ‘t’ is time taken for
change.
• A positive sign of the magnitude of acceleration shows increase in velocity and a
negative sign show decrease in velocity. If there is decrease in acceleration, it is called
Retardation. This means, rate of decrease in velocity is called Retardation.

10. SI unit of acceleration:
The SI unit of velocity is meter /second
The SI unit of time is second.
Acceleration in the case of Uniform Velocity:
 In the case of uniform velocity, the speed or direction of a
moving object is not changed and thus there is no change
in acceleration. Therefore, in the case of uniform velocity
acceleration will be zero.

11. SCALARS AND VECTORS
The motion of objects can be described by
words - words such as distance,
displacement, speed, velocity, and
acceleration. These mathematical quantities
which are used to describe the motion of
objects can be divided into two categories.
The quantity is either a vector or a scalar.

12. These two categories can be distinguished from one
another by their distinct definitions:
Scalars are quantities which are fully described by a
magnitude alone.
eg: displacement , velocity , force ,acceleration
etc.,
Vectors are quantities which are fully described by
both a magnitude and a direction.
eg : distance , mass ,time ,volume etc

14. First Equation of Motion:
The final velocity (v) of a moving object with uniform acceleration (a) after time, t.
 Let
 The initial velocity = u.
 Final velocity = v.
 Time = t
 Acceleration = a

15. Second Equation of Motion:
Distance covered in time (t) by a moving body.
Let,
Initial velocity of the object = u
Final velocity of the object = v
Acceleration = a
Time = t
Distance covered in given time = s

16. We know that, Distance covered (s) in given time = Average velocity x Time
Or, s = Average velocity x Time -----------------(iii)
After substituting the value of average velocity from equation (ii) we get
After substituting the value of ‘v’ from first equation of motion we get,

17. The third equation of motion is derived by substituting the value of time (t) from first equation of motion.
We know from first equation of motion, v=u+at
By substituting the value of ^' t^' from equation (v) we get

18. Different types of motion
Linear motion : when a body moves either in a straight line or along a
curved path, then we say that it is executing linear motion.
1. when a body moves in a straight line then the linear motion is
called rectilinear motion.
eg ., an athelete running a 100 meter race along a straight track is said
to be a linear motion or rectilinear motion.
2.when a body moves along a curved path then the linear motion is
called curvilinear motion.
eg., a planet revolving around its parent star

19. Other types of motion are :
Rotatory motion : A body is said to be in rotatory
motion when it stays at one place and turns round
and round about an axis.
example :a rotating fan,a spinning top, the earth.
Oscillatory motion : a body is said to be in oscillatory
motion when it swings to and fro about a mean
position.
example : the pendulum of a clock, the swing etc.,

20. Laws Of Motion

23. Derive 2nd law of motion
 As per 2nd law of motion
 Force x rate of change of momentum
F x m(v-u)/t
F=km(v-u)/t
Here K=1
so, F=m(v-u)/t
Therefore, (v-u)/t=a (from 1st equation of motion)
So, F=ma

25. CONSERVATION OF MOMENTUM
•Law of conservation of linear momentum is a extremely
important consequence of Newton's third law of motion in
combination with the second law of motion.
•According to law of conservation of momentumWhen two or
more bodies acts upon each other their total momentum
remains constant provided no external forces are acting
•So, Momentum is never created or destroyed.
•When this law is applied for a collision between two bodies,
the total momentum of the colliding bodies before collision is
equal to the total momentum after collision.
•We can apply this law for a collision between two vehicles.
This law is applicable for all types of collisions.

26. Consider two particles say A and B of mass m1
and m2 collide with each other and forces
acting on these particles are only the ones they
exert on each other.
Let u1 and v1 be the initial and final velocities of
particle A and similarly, u2 and v2for particle B. Let
the two particles be in contact for a time t.
So, Change in momentum of A=m1 (v1-
u1) Change in momentum of B=m2 (v2-u2 )

27.  During the collision, let A impart an average force equal to FBA on B and let B exert an
averageFAB on A. We know that from third law of motion FBA=-FAB (4)
Here,
canceling t on both sides and rearranging the equation we get
({m_1}{u_1} + {m_2}{u_2} = {m_1}{v_1} + {m_2}{v_2}) (5)
Now, ({m_1}{u_1} + {m_2}{u_2}) represents the total momentum of particles A and B before
collision and ({m_1}{v_1} + {m_2}{v_2}) represents the total momentum of particles after
collision. This means that
Total momentum before collision=total momentum after collision

28. • Equation 5 which ({m_1}{u_1} + {m_2}{u_2} = {m_1}{v_1} + {m_2}{v_2}) ,is
known as the law of conservation of momentum.
• Thus we conclude that when two particles are subjected only to their mutual
interactions ,the sum of the momentums of the bodies remains constant in time or we
can say the total momentum of the two particles does not change because of the any
mutual interactions between them.
• For any kind of force between two particles then sum of the momentum ,both before
and after the action of force should be equal i.e. total momentum remains constant.
• Law of conservation of linear momentum is one of the most fundamental and
important principle of mechanics.
• Once again ,the total momentum of two or any number of particles of interacting
particles is constant if they are isolated from outside influences (or no resultant external
forces is acting on the particles).

33. Examples of Motion as a
Universal Fact

35. Galaxy

38. Continents

39. Light propagates at 299,792,458 m/s, often approximated as
300,000 kilometers per second or 186,000 miles per second. The
speed of light (or c) is also the speed of all massless particles and
associated fields in a vacuum, and it is the upper limit on the
speed at which energy, matter, and information can travel. The
speed of light is the limit speed for physical systems.
In addition, the speed of light is an invariant quantity: it has the
same value, irrespective of the position or speed of the observer.
This property makes the speed of light c the natural measurement
unit for speed.

40. Graphical
Representation of
Motion

41. Distance – Time Graph
When an object is moving with uniform velocity, the slope of graph is always a
straight line. In other words slope of straight line of a distance-time graph shows
that object is moving with uniform velocity.
In the above graph, straight slope line shows that object is moving with uniform
velocity. Slope OB shows the velocity of the object.

42. Calculation of Velocity using distance-time graph
To calculate the velocity, let take two points A and B on the slope OB.
Draw one line parallel to y-axis and another parallel to x-axis from B.
Again draw a line parallel to y-axis and another parallel to x-axis from point A.
Let, line parallel to x-axis from point B cut at a point, S2 at y-axis.
Line parallel to x-axis from point A cut at point, S1 at y-axis.
Let, line parallel to y-axis from point B cut at t2 at x-axis.

43. Line parallel to y-axis from point A cut at t1 at x-axis.
Now, BC= Distance = S2 – S1 and AC = time = t2 – t1
We know that slope of the graph is given by the ratio of change in y-axis and change in X-axis.

44. Distance – Time Graph of a body moving with Accelerated
motion
When graph of distance Vs time is plotted for an object moving with accelerated motion, i.e. with increasing non-
uniform speed, the slope of graph will not be a straight line. The rising trend of slope shows the increasing trend of
velocity.

45. Velocity-Time
Graph

46. Velocity :– time graph of an object moving with uniform velocity
• The slope of a Velocity – time graph of an object moving in rectilinear motion with
uniform velocity is straight line and parallel to x-axis when velocity is taken along y-axis
and time is taken along x-axis.

47. Calculation of distance using velocity-time graph
Let two points A and B on the slope of graph.
Draw two lines parallel to y-axis AC from point A, and BD from point B.
Let point D at the x-axis (time axis) is t2 and point C is t1.
Let AB meet at ‘v’ at y-axis, i.e. object is moving with a velocity, v.
Thus, distance or displacement by the object is equal to the area of the rectangle (shaded) ABCD.
Thus, Area of ABCD = BD x DC
⇒ s = v (t2 – t1)
Since given object is moving with constant velocity along a straight line, thus displacement will be
equal to distance covered.
Therefore, Distance or Displacement = velocity X time interval.

48. Velocity – Time Graph of an object moving with uniform
acceleration
When velocity – time graph is plotted for an object moving with uniform acceleration, the
slope of the graph is a straight line.

49. • The pattern of slope of the graph shows that object is moving with uniform acceleration.
• Calculation of Displacement and Distance covered by the moving object using velocity time
graph:
• Let take two points, A and B at the slope of the graph.
• Draw a line from B to BD and another from point A to AE parallel to y-axis.
• Let AD meets at t2 and AE at t1 on the time axis.
• Thus, Distance covered by the object in the given time interval (t2 – t1) is given by the area of
ABCDE.

50. Velocity time graph of an object moving with uniform decreasing velocity
The slope of the velocity time graph of an object moving with uniform decreasing velocity with
uniform acceleration is a downwards straight line. The straight downward slope shows the
decreasing velocity with uniform acceleration, i.e. retardation.
Jig – zag line of slope of graph shows that the object is moving with non-uniform velocity.

51. Motion along a circular path:
 Motion of an object along a circular path is called circular motion.
Since, on a circular path the direction of the object is changing
continuously to keep it on the path, the motion of the object is
called accelerated motion.

52. Velocity in the case of circular motion.
 If the radius of circle is ‘r’
 Therefore, circumference = 2πr
 Let time ‘t’ is taken to complete one rotation over a circular path by any object
 Where, v = velocity, r = radius of circular path and t = time
 Motion of earth around the sun, motion of moon around the earth, motion of a top, motion of
blades of an electric fan, etc. are the examples of circular motion.