### Physics : CH # 4

**:**

__Motion__"When a body changes its position with respect to its surrounding so the body is said to be in the state of motion".

__Types Of Motion__*:*

There are three types of motion:

1, Linear or Translatory motion

2, Rotatory motion

3, Vibratory motion

__1. Linear or Translatory Motion:__

If a body moves in a straight path so the body is to be in Linear motion or Translatory motion.

**:**

__Example__A bus is moving on the road, A person is running on the ground.

**2. Rotatory Motion**

If a body spins or rotates from the fixed point ,so the body is to be in Rotatory motion.

**:**

__Example__The blades of a moving fan, The wheel of a moving car.

__3. Vibratory Motion:__To and fro motion about the mean point so the body is to be in Vibratory motion.

__Example__Motion of spring,motion of pendulum.

__Rest:__"When a body does not change its position with respect to its surrounding so the body is said to be in the state of rest".

__Example:__A book is laying on the table,A person is standing on floor,A tree in the garden.

__Speed:__"The distance covered by a body in a unit time is called speed."

**OR**

"The rate of change of distance is called speed."

__Formula:__*Speed =Distance/Time*

or V = S/t

__Unit:__The S.I unit of speed in M.K.S system is Meter/second or m/s

__Kinds Of Speed:__

__1. Uniform Speed:__If a body covers an equal distance in equal interval of time so the body is said to be in uniform speed.

__2. Variable Speed:__If a body does not cover an equal distance in equal interval of time so the body is said to be in variable speed.

__Velocity:__"The distance covered by a body in a unit time in a particular direction is called velocity."

**OR**

"The rate of change of displacement is called speed."

**OR**

"Speed in a definite direction is called velocity."

__Formula:__

Velocity = Displacement/Time

or V = S/t

__Unit:__The S.I unit of Velocity in M.K.S system is Meter/second or m/s

__Kinds Of Velocity:__

__1. Uniform Velocity:__If a body covers an equal distance in equal interval of time in a Constant direction so the body is said to be in uniform Velocity.

__2. Variable Velocity:__If a body does not cover an equal distance in equal interval of time in a particular direction so the body is said to be in variable velocity.

__Acceleration:__"The rate of change of velocity is called acceleration."

**OR**

"Acceleration depends upon the velocity if the velocity continuously increases or decreases the acceleration will be produced."

__1. Positive Acceleration:__If the velocity continuously increases then the acceleration will be positive.

__2. Negative Acceleration:__If the velocity continuously decreases then the acceleration will be negative.

__Formula:__*Acceleration = change of velocity/Time*

a = (Vf-Vi)/t

__Unit:__*The S.I unit of Velocity in M.K.S system is Meter/second+square or m/S*

^{2}

__Equation Of Motion:__The relationship of initial velocity, final velocity, acceleration, time,and linear distance.

__First Equation Of Motion:__Suppose an object moves with initial velocity "Vi" in a time "t" and covers a distance "S" in an acceleration "a" and the final velocity of an object becomes "Vf"

According to the definition of the acceleration "The rate of change of velocity is called acceleration"

i.e. Acceleration = Change of velocity/time

=> a = V

_{f}- Vi/t

__Derivation__

a = V

_{f}- Vi/t

or

at = V

_{f}- Vi

or

V

This equation is known as First Equation of motion.

_{f}= Vi + atThis equation is known as First Equation of motion.

__Second Equation Of Motion:__
Suppose an object moves with initial velocity "Vi" in a time "t" and covers a distance "S" in an acceleration "a" and the final velocity of an object becomes "Vf"

According to the definition of the acceleration "The rate of change of velocity is called acceleration".

i.e. Acceleration = Change of velocity/time

=> a = Vf - Vi/t

or

at = Vf - Vi

or

According to the definition of the acceleration "The rate of change of velocity is called acceleration".

i.e. Acceleration = Change of velocity/time

=> a = Vf - Vi/t

or

at = Vf - Vi

or

V

Substituting the average velocity:

V

The distance covered by the body in a unit:

S = V

Putting the value of Vav from equation 2:

S = [(Vi + V

Putting the value of Vf from equation 1:

S = [(Vi + Vi + at)/2] x t

S = [(2Vi + at)/2] x t

S = (Vi + at/2} x t

S = Vit + ½ at

This equation is known as 2nd Equation of motion.

_{f}= Vi + at -------------(1)Substituting the average velocity:

V

_{av}= (Vi + V_{f})/2 -----------(2)The distance covered by the body in a unit:

S = V

_{av}/tPutting the value of Vav from equation 2:

S = [(Vi + V

_{f})/2] x tPutting the value of Vf from equation 1:

S = [(Vi + Vi + at)/2] x t

S = [(2Vi + at)/2] x t

S = (Vi + at/2} x t

S = Vit + ½ at

^{2}This equation is known as 2nd Equation of motion.

**:**

__THIRD EQUATION OF MOTION__
Suppose an object moves with initial velocity "Vi" in a time "t" and covers a distance "S" in an acceleration "a" and the final velocity of an object becomes "Vf"

According to the definition of the acceleration "The rate of change of velocity is called acceleration".

Acceleration = Change of velocity/time

=> a = (V

=> at = V

or t = (V

Subsituting the average velocity:

Vav = (Vi + V

We know that:

V

=> S = V

Putting the value of Vav from equation 2 and value of t from eq 1:

S = [(Vi + V

S = Vi

or 2as = V

This equation is known as 3rd Equation of motion.

According to the definition of the acceleration "The rate of change of velocity is called acceleration".

Acceleration = Change of velocity/time

=> a = (V

_{f}- Vi)/t=> at = V

_{f }- Vior t = (V

_{f}- Vi)/a -------------(1)Subsituting the average velocity:

Vav = (Vi + V

_{f})/2 -----------(2)We know that:

V

_{av}= S/t=> S = V

_{av}x tPutting the value of Vav from equation 2 and value of t from eq 1:

S = [(Vi + V

_{f})/2] * [(V_{f}-Vi)/a]S = Vi

^{2}- Vf^{2}/2a since {(a+b) (a-b) = a^{2}- b^{2}}or 2as = V

_{f}^{2}- V_{i}^{2}This equation is known as 3rd Equation of motion.

__Acceleration Due To Gravity Or Free Falling Objects:__

"Galileo was the first scientist to appreciate that, neglecting the effect of air resistance, all bodies in free-fall close to the Earth's surface accelerate vertically downwards with the same acceleration: namely 9.8 m/s2"

__Example:__*If a ball is thrown vertically upward, it rises to a particular height and then falls back to the ground. However this is due to the attraction of the earth which pulls the object towards the ground"*

__Characteristic Of Free Falling Bodies:__

1, When a body is thrown vertically upward, its velocity continuously decreases and become zero at a particular height During this motion the value of acceleration is negative and Vf is equal to zero (a = -9.8m/s2 , Vf = 0).

2, When a body falls back to the ground , its velocity continuously increases and become maximum at a particular height During this motion the value of acceleration is positive and Vi is equal to zero (a = 9.8m/s2 , Vi = 0).

3, Acceleration due to gravity is denoted by a and its value is 9.8m/s2 .

4, Equation of motion for the free-falling bodies be written as,

V

_{f}= Vi + gt

h = Vit + 1/2 gt

^{2}

2gh = V

_{f}

^{2}- Vi

^{2}

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