kinematics...the shape of the speed-time graph is curve (or zigzag) when the body has variable...

UNIT 2 (KINEMATICS) PHYSICS – IX

Prepared by: Ms. Maimoona Altaf

Kinematics

Solved Exercise

MCQ's

2.1) Encircle the correct answer from the given choices:

i) A body has translatory motion if it moves along a

A. Straight line B. Circle C. Line without rotation D. Curved path

ii) The motion of a body about an axis is called

A. Circular motion B. Rotatory motion C. Vibratory motion D. Random motion

iii) Which of the following is a vector quantity?

A. Speed B. Distance C. Displacement D. Power

iv) If an object is moving with constant speed then its distance-time graph will be a straight line.

A. Along time-axis B. Along distance-axis

C. Parallel to time-axis D. Inclined to time-axis

v) A straight line parallel to time-axis on a distance-time graph tells the object is

A. Moving with constant speed B. At rest

C. Moving with variable speed D. In motion

vi) The speed-time graph of a car is shown in the figure, which of the following statement is true?

A. Car has an acceleration of 1.5 ms-2 B. Car has constant speed of 7.5 ms-1

C. Distance travelled by the car is 75 m D. Average speed of the car is 15 ms-1

v (ms-1

)

15

10 0

t (s)



vii) Which of the following graphs is representing uniform acceleration?

A. B.

C. D.

viii) By dividing displacement of a moving body with time, we obtain

A. Speed B. Acceleration C. Velocity D. Deceleration

ix) A ball is thrown vertically upward. Its velocity at the highest point is:

A. -10 ms-1 B. Zero C. 10 ms-2 D. None of these

x) A change in position is called:

A. Speed B. Velocity C. Displacement D. Distance

xi) A train is moving at a speed of 36 kmh-1. Its speed expressed in ms-1 is:

A. 10 ms-1 B. 20 ms-1 C. 25 ms-1 D. 30 ms-1

xii) A car starts from rest. It acquires a speed of 25 ms-1 after 20 s. The distance moved by the car during this time is:

A. 31.25 m B. 250 m C. 500 m D. 5000 m

Exercise Questions

2.2) Explain translatory motion and give examples of various types of translatory motion.

Translatory motion:

In translatory motion, a body moves along a line without any rotation. The line may be straight or curved.

Example:

Aeroplane flying straight in air, motion of the Earth around the Sun and motion of insects and birds, etc.

t t

t t

d d

v v



There are three types of translatory motion:

i) Linear motion:

Straight line motion of a body is known as its linear motion.

The motion of objects such as a car moving on a straight and level road, aeroplane flying straight in air and objects falling vertically down are the examples of linear motion.

ii) Circular motion:

The motion of an object in a circular path is known as circular motion.

A stone tied at the end of a string can be made to whirl. The stone moves in a circle and thus has circular motion. Toy train moving on a circular track. A bicycle or a car moving along a circular track possesses circular motion. Motion of the Earth around the Sun and motion of the moon around the Earth are also the examples of circular motion.

iii) Random motion:

The disordered or irregular motion of an object is called random motion.

The motion of insects and birds are irregular. Thus, motion of insects and birds is random motion. The motion of dust or smoke particles in the air is also random motion. The



Brownian motion of a gas or liquid molecules along a zigzag path is also an example of random motion.

2.3) Differentiate between the following:

i) Rest and motion.

Rest: A body is said to be at rest, if it does not change its position with respect to its surroundings.

Motion: A body is said to be in motion, if it changes its position with respect to its surroundings.

The state of rest or motion of a body is relative. For example, a passenger sitting in a moving bus is at rest because he/she is not changing his/her position with respect to other passengers or objects in the bus. But to an observer outside the bus, the passenger and the objects inside the bus are in motion.

ii) Circular motion and rotatory motion.

Circular motion: The motion of an object in a circular path is called circular motion.



Rotatory motion: The spinning motion of a body about its axis is called rotatory motion.

For example, Earth revolves around the Sun, in the same time it also rotate about its axis.

iii) Distance and displacement.

Distance Displacement

i) Length of a path between two points is called the distance between those points.

i) Displacement is the shortest distance between two points.

ii) Distance is a scalar quantity. ii) Displacement is a vector quantity.

iii) Distance is denoted by “S”. S = vt

SI unit of distance is metre (m).

iii) Displacement is denoted by “d”. d = vt

SI unit of displacement is metre (m).

Distance S (dotted line) and displacement d (dark line) from points A to B.

iv) Speed and velocity.

Speed Velocity

i) The distance covered in unit time is known as speed.

i) The rate of displacement of a body with respect to time is called velocity.

ii)

ii)

iii) It is a scalar quantity. iii) It is a vector quantity.

v) Linear and random motion.

Linear motion: Straight line motion of a body is known as its linear motion.

Examples: The motion of objects such as a car moving on a straight and level road is linear motion. Aeroplane flying straight in air and objects falling vertically down are also the examples of linear motion.



Random motion: The disordered or irregular motion of an object is called random motion.

Examples: The motion of insects and birds are irregular. Thus, motion of insects and birds is random motion. The motion of dust or smoke particles in the air is also random motion. The Brownian motion of a gas or liquid molecules along a zigzag path is also an example of random motion.

vi) Scalars and vectors.

Scalars Vectors

Physical quantities which are completely described by their magnitude only are known as scalar.

Physical quantities which are completely described by their magnitude and direction as well are known as vector.

Example: speed, distance, time, etc. Example: force, displacement, velocity, etc.

2.4) Define the terms speed, velocity, and acceleration.

Speed: Speed is defined as change of distance per unit time. It is a scalar quantity.

Its SI unit is meter per second (ms-1).

Velocity: Velocity is defined as change of displacement per unit time. In other words, velocity is speed in a given direction. It is a vector quantity.

Its SI unit is also meter per second (ms-1).

Acceleration: Acceleration is defined as change of velocity per unit time. It is a vector quantity.

Its SI unit is meter per second per second (ms-2).



2.5) Can a body moving at a constant speed have acceleration?

Yes, when a body is moving with constant speed, the body can have acceleration if its direction changes. For example, if the body is moving along a circle with constant speed, it will have acceleration due ti the change of direction at every instant.

2.6) How do riders in a Ferris wheel possess translatory motion but not rotatory motion?

Riders in a Ferris wheel possess translator motion because their motion is in a circle without rotation.

2.7) Sketch a distance-time graph for a body starting from rest. How will you determine the speed of a body from this graph?

When a body starts from rest then the distance-time graph is a straight line. The slope of the line is numerically equal to the speed of the body.

Consider two points A and B on the graph.

Speed of the object = Slope of line AB

=

The speed found from the graph is 2 ms-1.

2.8) What would be the shape of a speed-time graph of a body moving with variable speed?

The shape of the speed-time graph is curve (or zigzag) when the body has variable speed.

2.9) Which of the following can be obtained from speed-time graph of a body?

i) Initial speed.

ii) Final speed.

iii) Distance covered in time t.

iv) Acceleration of motion.

All the given factors can be obtained from speed-time graph of a body.

2.10) How can vector quantities be represented graphically?

A vector can be represented graphically drawing a straight line with an arrow head at one end. The length of the line tells the magnitude and arrow head shows the direction of the vector.



2.11) Why vector quantities cannot be added and subtracted like scalar quantities?

The scalar quantities obey the rules of arithmetic and ordinary algebra because scalar quantities have no direction. In addition of vectors, both magnitude and direction are involved. Therefore, vectors cannot be added by simple method of scalar addition. So vectors are added by head to tail rule.

2.12) How are vector quantities important to us in our daily life?

It would be meaningless to describe vectors without direction. For example, distance of a place from reference point is insufficient to locate that place. The direction of that place from reference point is also necessary to locate it.

Some of the everyday activities that involve vectors are given below:

Breathing (your diaphragm muscles exert a force that has a magnitude and direction)

Walking (you walk at a velocity of around 7 km/h in the direction of the kitchen)

Going to school (the bus has a length of about 300 m and is headed towards your school)

Lunch (the displacement from your class room to the canteen is about 50 m in a northerly direction)

Vectors are important as they describe physical processes in the real world, and without understanding them, we cannot understand how the real world works. Imagine how difficult it would be for an air traffic controller if he didn’t understand vectors when directing planes speeds and directions.

2.13) Derive equations of motion for uniformly accelerated rectilinear motion.

Calculations involving the displacement, velocity, acceleration and time of motion of a moving body use the equations of motion. These equations are derived from the definitions of average velocity and acceleration.

For a body undergoing uniform acceleration,

Displacement = average velocity × time

1st Equation of Motion

From equation (ii),



2nd Equation of Motion

Substituting equation (iv), , in equation (iii),

3rd Equation of Motion

From equation (iii),

, and from equation (iv), . Multiplying these

equations together gives

2.14) Sketch a velocity-time graph for the motion of the body. From the graph explaining each step, calculate total distance covered by the body.

In a speed-time graph, time is taken along x-axis and speed is taken along y-axis. DISTANCE TRAVELLED BY A MOVING OBJECT The area under a speed-time graph represents the distance travelled by the object. If the motion is uniform then the area can be calculated using appropriate formula for geometrical shapes represented by the graph.

Total distance travelled = area under the graph (trapezium OABC)

=

=

=

=



Problems

2.1) A train moves with a uniform velocity of 36 kmh-1 for 10 s. Find the distance travelled by it.

Data:

Formula Used:

Solution:

2.2) A train starts from rest. It moves through 1 km in 100 s with uniform acceleration. What will be its speed at the end of 100 s.

Data:

Formula Used:

Solution:

Now using 1st equation of motion,



2.3) A car has a velocity of 10 ms-1. It accelerates at 0.2 ms-2 for half minute. Find the distance travelled during this time and the final velocity of the car.

Data:

Formula Used:

Solution:

For final velocity using 1st equation of motion,

2.4) A tennis ball is hit vertically upward with a velocity of 30 ms-1. It takes 3 s to reach the highest point. Calculate the maximum height reached by the ball. How long it will take to return to ground?

Data:



Formula Used:

Solution:

As the ball moves with uniform acceleration in vertical motion, so time taken by the ball in both directions will be same.

Total time taken to return the ground = Time taken upwards + Time taken downwards

Total time taken to return the ground = 3 s + 3 s

Total time taken to return the ground = 6 s

2.5) A car moves with uniform velocity of 40 ms-1 for 5 s. It comes to rest in the next 10 s with uniform deceleration. Find (i) deceleration (ii) total distance travelled by the car.

Data:

Formula Used:



Solution:

i) Deceleration:

ii) Total distance travelled:

As we know that,

Now from 2nd equation of motion, we have:

2.6) A train starts from rest with an acceleration of 0.5 ms-2. Find its speed in kmh-1, when it has moved through 100 m.

Data:

Formula Used:

Solution:

From 3rd equation of motion, we have



√

In kmh-1

2.7) A train starting from rest, accelerates uniformly and attains a velocity 48 kmh-1 in 2 minutes. It travels at this speed for 5 minutes. Finally, it moves with uniform retardation and is stopped after 3 minutes. Find the total distance travelled by the train.

Solution:

2.8) A cricket ball is hit vertically upwards and returns to ground 6 s later. Calculate (i) maximum height reached by the ball. (ii) initial velocity of the ball.

Data:



Formula Used:

Solution:

As the ball moves with uniform acceleration in vertical motion, so time taken by the ball in both directions will be same.

Total time taken to return the ground = Time taken upwards + Time taken downwards

6 s = Time taken upwards + Time taken downwards

As, Time taken upwards = Time taken downwards

Total time taken to return the ground = 2 × Time taken upwards

So, Time taken upwards =

From first equation of motion, we have

Now from second equation of motion, we have

2.9) When brakes are applied, the speed of a train decreases from 96 kmh-1 to 48 kmh-1 in 800 m. How much further will the train move before coming to rest? (Assuming the retardation to be constant).

Data:

Initial velocity =

Final velocity =

Distance = S = 800 m

Acceleration = a = ?



Formula Used:

Solution:

Now for further journey

Initial velocity =

Final velocity =

Deceleration = a = -0.3345 ms-2

Distance = S = ?

2.10) In the above problem, find the time taken by the train to stop after the application of

brakes.

Data:

Initial velocity =

Final velocity =

Acceleration = a = -0.3345 ms-2

Time = t = ?

Formula Used:

Solution:

Hence the time to apply brakes is 80 s.

Extra MCQ’s

1. Speed × time is equal to:

A. A. displacement B. B. distance C. C. velocity D. position

2. Scalar quantities are completely described by their: A. unit B. area C. direction D. magnitude



3. If a body does changes its position with respect to its surroundings, it is said to be at:

A. distance B. position C. rest D. motion 4. A quantity described by magnitude and direction both is called:

A. scalar B. vector C. unit D. physical 5. Gravitational acceleration for bodies moving up is:

A. positive B. negative C. zero D. always equal to one a 6. Total length of path is named:

A. displacement B. distance C. length D. path 7. Rest state and motion of body are:

A. non relative B. not related C. relative D. none of these

8. A tennis ball hits vertically upward with velocity of 25ms−1 and takes 4 s to reach highest point.

maximum height reached by ball is:

A. 45 m B. 55 m C. 30 m D. 50 m

9. Spinning of body about its axis is:

A. rotatory B. circular C. translational D. none of these

10. Quantities between which a graph is plotted are known as:

A. constants B. co-efficients C. surds D. variables

11. If a body does not change its position with respect to its surroundings, it is said to be at:

A. rest B. motion C. distance D. position

12. A cyclist completes half round of a circle track of radius 420 metres in 3 minutes. Its speed will

be:

A. 5 ms−1 B. 8 ms−1 C. 10 ms−1 D. 7.33 ms−1

13. Distorted motion of an object is:

A. circular B. random C. vibratory

D. vibratory and

translational

14. Velocity is rate of change of:

A. displacement B. distance C. force D. none of these

15. Distance covered by an object in unit time is called its:

A. speed B. velocity C. displacement D. position

16. Study of motion of an object without discussing cause of motion is known as:

A. kinematics B. dynamics C. trinamics D. friction

17. Negative acceleration is called:

A. friction B. retardation C. uniform acceleration D. variable acceleration

18. Height of tower when stone dropped from it reaches ground in 5 s is:

A. 130 m B. 125 m C. 150 m D. 200 m

19. Motion of riders in Ferris wheel is:

A. rotatory B. translational C. non relative D. none of these

20. In terms of velocity, symbol vf is used for:

A. final velocity B. initial velocity C. negative velocity D. total velocity



21. Shortest distance between 2 points which also has direction and magnitude is termed as:

A. position B. velocity C. displacement D. distance

22. Time taken by a train to slow down from 80 kmh-1 to 20 kmh-1 with a uniform deceleration of

2 ms-2 is:

A. 9 s B. 10 s C. 8.3 s D. 8.4 s 23. Rate of change of velocity is called:

A. speed B. distance C. force D. acceleration 24. Types of motion are:

A. 2 B. 3 C. 4 D. 5 25. If velocity of a body increases with time, then its acceleration is:

A. zero B. positive C. negative D. none of these

26. Length of a path between 2 points is called:

A. displacement B. distance C. position D. velocity

27. If a body doesn't change its position with respect to its surroundings then it’s in state of:

A. motion B. rest C. equilibrium D. weightlessness

28. A car is moving at a speed of 36 kmh−1. Its speed expresses in ms−1 is:

A. 25 ms−1 B. 10 ms−1 C. 20 ms−1 D. 30 ms−1

29. Displacement⁄time taken is equal to:

A. uniform speed B. velocity C. speed D. distance

30. A brick is dropped from top of a building. If it hits ground after 6 seconds, height of building

will be:

A. 120 metres B. 150 metres C. 110 metres D. 180 metres

31. Location of a place or a point with respect to some reference point (origin) is known as:

A. velocity B. rest C. displacement D. position

32. Motion of an object in a circular path is called:

A. random motion B. vibratory motion C. circular motion D. linear motion

33. Reference point is taken as:

A. origin B. anywhere on x-axis C. anywhere on y-axis D. in between two

coordinates

34. If a body covers equal displacement in equal intervals of time however short interval may be,

then it has:

A. uniform velocity B. uniform speed C. non-uniform speed D. uniform acceleration

35. If a body covers equal distance in equal intervals of time then its speed is:

A. variable B. uniform C. equal D. constant

36. An athlete completes its 200 metre race in 25 seconds. Its average speed will be: A. 6 ms−1 B. 10 ms−1 C. 8 ms−1 D. 5 ms−1

37. A train moves with a uniform velocity of 27 kmh−1 for 15 s. distance covered by it is:

A. 112.5 m B. 115 m C. 120 m D. 135 m

38. If a body doesn't rotates then its motion is:

A. Vibratory B. rotatory C. both A and B D. Translational



39. If line of motion is curved then body exhibit:

A. linear motion B. rotatory motion C. translational motion D. vibratory motion

40. A bus starts from rest with acceleration of 0.5 ms−2. If it has moved through 100 m, then its

speed will be:

A. 23 kmh−1 B. 25 kmh−1 C. 34 kmh−1 D. 36 kmh−1

41. If a body covers equal distances in equal intervals of time however short interval may be, then

it has:

A. uniform velocity B. uniform speed C. uniform acceleration D. non-uniform velocity

42. Distance covered ⁄ time taken is equal to:

A. speed B. velocity C. displacement D. position 43. Motion of a butterfly is an example of: A. vibratory motion B. circular motion C. linear motion D. random motion

44. In a graph, in which time is taken along X-axis and speed is taken along Y-axis is called:

A. speed-time graph B. pi chart C. distance graph D. distance-time graph

45. Velocity with which a paratrooper comes to ground is called:

A. average velocity B. variable velocity C. constant velocity D. terminal velocity

46. Gravitational acceleration is acceleration of bodies:

A. on ground B. in air C. freely falling D. none of these

47. Flying speed of a falcon is:

A. 100 kmh-1 B. 200 kmh-1 C. 50 kmh-1 D. 500 kmh-1

48. A stone is dropped from top of a building which is 180 metres high. If stone hits ground after 6

seconds, its final velocity will be:

A. 40 ms−1 B. 50 ms−1 C. 60 ms−1 D. 110 ms−1

49. If object is at rest then distance-time graph is:

A. straight line parallel

to y-axis B. variable

C. straight line parallel

to x-axis D. parabolic

50. Gravitational acceleration for bodies falling down freely is:

A. positive B. negative C. zero D. always equal to one a

51. If body has equal changes in velocity in equal intervals of time however short interval may be,

then it has:

A. uniform velocity B. uniform speed C. distance D. uniform acceleration

52. Among following scalar quantity is:

A. length B. mass C. volume D. all of these

53. Rate of displacement of a body is called its:

A. non-uniform speed B. non-uniform velocity C. velocity D. speed

54. Motion of a baby in a swing is an example of:

A. circular motion B. rotatory motion C. random motion D. vibratory motion

55. Mass, length, speed, work, time and energy are examples of:

A. velocity B. scalar C. vector D. displacement



56. Equations of motion for bodies moving with uniform acceleration are of:

A. 2 types B. 3 types C. 4 types D. 5 types

57. Change in velocity⁄time taken is equal to:

A. speed B. distance C. displacement D. acceleration

58. Motion of a steering wheel is an example of:

A. vibratory motion B. circular motion C. rotatory motion D. linear motion

59. A bus accelerates at 1 ms−2 from an initial velocity of 4 ms−1 for 10s. Distance moved in that

time will be:

A. 90 metre B. 25 metre C. 60 metre D. 72 metre

60. Velocity, displacement, force, momentum are examples of:

A. energy B. scalar C. vector D. length

61. In distance-time graph time is taken on:

A. y-axis B. x-axis C. z-axis D. in between two

coordinates

62. A motion in which a body moves along a line without any rotation is known as:

A. translatory motion B. rotatory motion C. vibratory motion D. rest

63. Disordered or irregular motion of an object is called:

A. vibratory motion B. circular motion C. linear motion D. random motion

64. Quantity whose value varies with independent quantity is termed as:

A. negative quantity B. dependent quantity C. fixed quantity D. zero quantity

65. Numerical value with an appropriate unit is called:

A. rate B. magnitude of

quantity C. amount D. position

66. A physical quantity which can be completely described by its magnitude and direction is

called:

A. scalar B. vector C. displacement D. velocity

67. Acceleration of freely falling bodies is known as:

A. Galileo acceleration B. going acceleration C. graphical

acceleration

D. gravitational

acceleration

68. A straight line parallel to time-axis on a distance-time graph tells that object is:

A. at rest B. in motion C. moving with

constant speed

D. moving with variable

speed

69. A ball is thrown vertically upward. Its velocity at highest point is:

A. zero B. 10 ms−1 C. 15 ms−1 D. 20 ms−1

70. (Final velocity - initial velocity) is called:

A. position B. acceleration C. change in velocity D. displacement

71. A passenger John is sitting in a moving car, as per an observer outside car, he is at:

A. position B. rest C. motion D. displacement



72. A cyclist completes half round of a circle track of radius 420 metres in 3 minutes. Its velocity

will be:

A. 4.67 ms−1 B. 5.33 ms−1 C. 2.8 ms−1 D. 3.5 ms−1

73. A car starts from rest. It moves through 2 km in 100 s with uniform acceleration. Its speed at

end of 100 s will be:

A. 80 ms−1 B. 20 ms−1 C. 40 ms−1 D. 10 ms−1

74. Velocity of ball at highest point when its thrown vertically upward is:

A. -10 ms-1 B. 10 ms-2 C. 8 ms-1 D. zero

75. Quantities between which graph is plotted is called:

A. scalars B. vectors C. variables D. none of these

76. To and fro motion of a body about its mean position is termed as:

A. random motion B. vibratory motion C. circular motion D. rotatory motion

77. A bus starts from rest. Its velocity becomes 30 ms−1 in 8s. Its acceleration will be:

A. 3 ms−2 B. 5 ms−2 C. 2 ms−2 D. 3.5 ms−2

78. Velocity of cyclist when he completes half round of a circular track of radius 318 m in 1.5 min

is:

A. 10 ms-1 B. 8 ms-1 C. 7.07 ms-1 D. 9 ms-1

79. Alex is walking at rate of 2km/h towards east, it is an example of:

A. vector B. scalar C. length D. energy

80. Straight line motion of a body is known as:

A. circular motion B. linear motion C. random motion D. vibratory motion

81. Value of gravitational acceleration is approximately:

A. 15 ms−2 B. 25 ms−2 C. 10 ms−2 D. 5 ms−2

82. A spinning motion of a body about its axis is called its:

A. rotatory motion B. vibratory motion C. circular motion D. linear motion

83. In terms of velocity, symbol vi is used for:

A. initial velocity B. negative velocity C. total velocity D. final velocity

84. Gravitational acceleration is denoted by:

A. a B. g C. r D. G

85. If a car is moving at a velocity of 30 ms−1 then slows down uniformly to 20ms−1 in 6s. Its

retardation will be:

A. 5 ms−2 B. 2.33 ms−2 C. 1.67 ms−2 D. 4 ms−2

86. If velocity of a body decreases with time, then its acceleration is:

A. zero B. positive C. negative D. none of these

87. A passenger John is sitting in a moving car, so with respect to other passengers he is at:

A. rest B. motion C. displacement D. position

88. Third equation of motion can be written as:

A. Vf = Vi + at B. 2aS = V2f - V

2i C. 2aS = Vf - Vi D. none of these



89. Deceleration or retardation are synonyms of:

A. positive acceleration B. negative acceleration C. zero acceleration D. speed

90. Displacement is defined as:

A. the longest distance

between two points

B. the distance

between two points

C. the shortest

distance between two

points

D. all of these

91. Rate of change of velocity of a body is called its:

A. displacement B. acceleration C. speed D. distance

92. Children playing on see-saw exhibit:

A. translational motion B. rotatory motion C. linear motion D. vibratory motion

93. A train starts from rest. It acquires a speed of 25 ms−1 after 20 s. Total distance is:

A. 500 m B. 31.25 m C. 300 m D. 250 m

94. If a car is traveling at 8 ms−1 accelerates uniformly at 2 ms−2, its velocity after 5 seconds will

be:

A. 20 ms−1 B. 23 ms−1 C. 25 ms−1 D. 28 ms−1

95. Motion of Earth around Sun is an example of:

A. random motion B. vibratory motion C. circular motion D. linear motion

96. Rate of change of distance is:

A. velocity B. force C. position D. speed

97. If a car is moving at 30 ms-1 and uniformly slows down to 15 ms-1 in 5s then its deceleration is:

A. - 3 ms-1 B. - 4 ms-1 C. 5 ms-1 D. 21 ms-1

98. A vector quantity among following is:

A. velocity B. force C. both A and B D. energy

99. A bus moving in a straight and leveled road is in:

A. linear motion B. vibratory motion C. circular motion D. random motion

kinematics...the shape of the speed-time graph is curve (or zigzag) when the body has variable...

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