CHAPTER 4- KINEMATICS
Kinematics:The study of movement without reference to the forces that cause the movement.
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
Linear Motion: Movement with constant acceleration is known as linear 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 a spring.
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 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
or
a = (Vf-Vi)/t
UNIT
The S.I unit of Velocity in M.K.S system is Meter/second + square
or
m/S2
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 = Vf – Vi/t
DERIVATION
a = Vf – Vi/t
at = Vf – Vi
or
Vf = Vi + at
SECOND EQUATION OF MOTION
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
at = Vf – Vi
or
Vf = Vi + at ————-(1)
Substituting the average velocity:
Vav = (Vi + Vf)/2 ———–(2)
The distance covered by the body in a unit:
S = Vav/t
Putting the value of Vav from equation 2:
S = [(Vi + Vf)/2] * t
Putting the value of Vf from equation 1:
S = [(Vi + Vi + at)/2] * t
S = [(2Vi + at)/2] * t
S = (Vi + at/2} * t
S = (Vit + 1/2at2) {Here 2 is the square of the time “t”. Don’t write this sentence in the examination}
THIRD 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 = (Vf – Vi)/t
=> at = Vf – Vi
or
t = (Vf – Vi)/a ————-(1)
Substituting the average velocity:
Vav = (Vi + Vf)/2 ———–(2)
We know that:
Vav = S/t
=> S = Vav * t
Putting the value of Vav from equation 2 and value of t from eq 1:
S = [(Vi + Vf)/2] * [(Vf-Vi)/a]
S = Vi2 – Vf2/2a since {(a+b) (a-b) = a2 – b2}
or
2as = Vf2 – Vi2
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,
Vf = Vi + gt
h = Vit + 1/2 gt2
2gh = Vf2 – Vi2
