kinematics

Page 1

Physics th

Class 9

Written by Shahid Ahmad Bangash E-mail address: Mr_shahid_ahmad@yahoo.com

Mobil No: 0314-9132833

Chapter 3

Kinematics Kinematics (from Greek, kinein, to move) the branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion.

Motion: A body said to be in motion if it is changing its position with respect to its surroundings. Example: 1) A flying bird 2) A moving car 3) A running boy Rest: A body said to be at rest if it does not change its potion with respect to it s surroundings. Example: 1) A bus standing at stop 2) a laying stone on earth

Types of motion: there are three types of motion. 1) Translatory motion 2) Rotatory motion 3) Vibratory motion

1)

Translatory motion: A motion of body in which all parts of the moving body move toward the same direction. Or When body is moving in a line, tis motion is called translatory motion. Example: a flying bird, a moving bus on road, motion of boat

2)

Rotatory motion: Spinning or turning motion that takes place around an axis, without a change in linear position. Or When a body moves or rotates such that its distance from the fix point remains constant Example: moving blades of fan, wheel of a bicycle

2

Chapter 3 3)

Vibratory motion:: to and fro motion of a body along same path about mean position is called vibratory or oscillatory motion. Example:: motion of simple pendulum, motion of mass attach spring

Displacement: A displacement is the shortest distance from the initial to the final position of a point or the shortest or straight distance between two points along which a body move is called displacement. Symbol: displacement is denoted by

Unit:: the unit of displacement is “meter” denoted by “m”. Vector quantity:: it is a vector quantity

Speed: the distance of a body movie in a unit time or speed is the rate of change of distance. “ Symbol: it is donate by “v”.

Formula:

or

speed=

Unit:: unit of speed is meter per second, denoted by Scalar quantity:: it is scalar quantity. quantity

1) Average speed:: the total distance covered by a body divided by total time is called the average speed. Symbol: it is donate by”

Formula:

”

Average verage speed =

Unit: unit of average speed is meter per second, denoted by

3

.

Chapter 3 2) Uniform speed: if a body covers equal distance in equal interval of time, than it is called uniform speed. Formula:

uniform speed=

or

Unit: unit of uniform speed is meter per second, denoted by .

3) Variable speed: if a body covers unequal distance in equal interval of time, then speed of the body is said to be variable. 4) Instantaneous speed: it is defined as the speed of body at any instant of time.

Formula: instantaneous speed=

Unit: unit of instantaneous speed is meter per second, denoted by .

Velocity: rate of change of displacement is called velocity Or Speed of a body in particular direction is called velocity Symbol: it is denoted by “ �.

Formula:

!" #$%&' ( (" '

) *

+

Unit: unit of velocity is same as speed which is “meter per second�, .

Vector Quantity: velocity is vector quantity.

Average velocity: the total displacement divide by total time is called average velocity. )* Symbol: Average velocity is denoted by

4

Chapter 3 Formula:

Average

))* )))* /0 (,(%$ !" #$%&' ( , . (,(%$ (" '

Unit: unit of average velocity is “meter per second�, .

Uniform velocity: the velocity of a body is said to be uniform when the speed as well as the direction of the body do not change with time.

Instantaneous velocity: the instantaneous velocity of a moving body is defined as the time rate of change of displacement.

Formula:

) * + 12

Variable Velocity: velocity is variable if a body is changing its speed or direction or both motion of variable velocity is called accelerated motion.

3*

Acceleration: Rate of change of velocity is called acceleration. Symbol: it is denoted by Formula: Acceleration = Where <=

&4%56' ,7 8'$,&"(9; (" ' "5(':8%$

Unit: the unit of acceleration is meter per second >0 @ Vector Quantity: it is vector quantity.

5

?

)))))* 3* ; (

Chapter 3 Positive acceleration: the acceleration that is produced by increasing the speed is called positive acceleration or simply acceleration. The positive acceleration is always in the direction of motion.

Negative acceleration: the acceleration that is produced by decreasing the sped is called negative acceleration or deceleration. The negative acceleration is always in the opposite direction of motion.

Uniform acceleration: acceleration of constant magnitude and unchanging direction is called uniform or constant acceleration.

Average acceleration: the total change in velocity divided by total time is called average acceleration. Formula:

)))))* )* . ;( -%

Unit: unit is meter per second >;? A

Frist equation of motion 87B "C %(

Suppose a body is moving with some initial velocity “ D � after some time “t� its velocity changes and becomes E . Change in velocity

Acceleration.

EFG

3

GEFGD

but change in velocity in unit time is called

Multiplying “t� on both sides.

H3

Adding “Vi� on both sides

6

GEFGD

H

3 < =

Chapter 3

I 3 < = I I 3 <

< I 3 Hence proved " I

Second Equation of motion

@ 3 K J

Suppose a body is moving with some initial velocity L L after some timeL Lits velocity changes and become L <L so the distance is covered by the body is directly proportional to time L L

- . ;(

‌‌‌. (1)

- .

So average velocity and is -

.

Putting the value of <v> in equation 2

M

From first equation of motion

<I @

<I N (‌‌‌. (3) @

< " I 3

Putting the value of L <L in equation 3

7

‌‌‌. (2)

" I 3 I " O P(

@

@ " I 3 @ R( Q @

Chapter 3

@ " 3 @ I @ @ 3 @ " I @

" I

Third Equation of motion @3?

J @ 3 K

E A = D

A

Suppose a body is given some initial velocity L Lafter some time L Lits velocity

changes and become L <Lso the distance s covered by the body is directly proportional to timeL L.

- . ;( - .

So average velocity and is -

.

Putting the value of <v> in equation 2

M

From first equation of motion (

‌‌‌. (2)

<I N (‌‌‌. (3) @ 87 F "

Putting the value of L L in equation (3)

M

<I @

‌‌‌. (1)

%

<I 87 = " NS T % @

< @ = @ ? U V @3

8

Chapter 3

Multiplying by @3 on both sides

E A = D A P H @3 @3 H ? O @3

Short Question answer

@3? E A = D A

Q what is Acceleration due gravity? Ans: the acceleration of a freely falling body is called acceleration due to gravity.it is denoted by g, it is denoted by g its value is found to be 9.8m/s2. We take the g value positive when object move upward and take negative when move downward.

Q: Does the speedometer of a car show the speed or velocity of the car? Ans: the speedometer of a car tells us how slow or fast a car is moving. It gives us no detail about the direction of car. Thus the speedometer of a car shows only the speed of a car

Q: A body is thrown vertically upward. What is tis acceleration? Ans: when object move upward than the magnitude of acceleration is negative we can write g= - 9.8m/s2

Q: under what condition a body whose velocity is directed towards east has acceleration directed west? Ans:if a body is coming to rest by applying brakes slowly, then it is possible that its velocity is directed towards east, his acceleration directed towards west.

Q: what is acceleration of a body moving with uniform velocity? Ans: when velocity is uniform than acceleration zero because we know that change in velocity in unit time is called acceleration. In this condition the velocity is not going to change so acceleration will be zero. Mathematically: In uniform velocity the initial velocity is equal to finial velocity . Initial velocity =

Final velocity = < 9

Chapter 3 From first equation of motion So <

3

3

GEFGD

= W because < is equal to X

3 WYZ[@

Q: A body is moving with uniform speed can it have acceleration? Explain? Ans: in order to explain this case, we have two conditions. 1) If a body moves in a straight path with uniform speed than there will be no acceleration. 2) If a body moves in a circular path with uniform speed then it will have some acceleration, because the direction of velocity changes at every point, due to which acceleration is produced.

Written by Shahid Ahmad Bangash E-mail address: Mr_shahid_ahmad@yahoo.com

Mobil No: 0314-9132833

10

Chapter 3

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