NTRODUCTION
MOTION-It is change in position with respect to time.
Rectilinear Motion – Motion in straight line .
Circular Motion –Motion in circular path .
When an object fall freely is called Free Fall (or initial velocity is zero vertically).
KINEMATICS – Study about describe motion without going to cause of motion.
Types of motion – 2
- Uniform Motion –An object cover equal distance in equal interval of time.
- Non-Uniform Motion-An object cover unequal distance in equal interval of time .
INSTANTANEOUS VELOCITY AND SPEED-
The average velocity tell that how fast an object
moving but not tell the speed at a instant of time.
Instant Velocity- Velocity at a instant(or a point) of time .
In language of Calculus, R.H.S. have a differential coefficient of ‘x’ to time ‘t‘ and denoted by dx/dt(x is a function of time).
We obtain the value at an instant either graphically or numerically . But it is difficult to show this graphically ,so we numerical method .
For uniform motion , velocity is same as the average velocity at all instant .
SOME IMPORTANT POINTS –
ACCELERATION –
Rate of change in velocity with respect to time.
It is vector quantity. And its formula is acc.=change in velocity/time .
Its SI unit and dimension is m/sec2 and [M0L1T-2].
Instantaneous Acceleration is acceleration at an instant of time .
VELOCITY-
Ratio of displacement with respect to time.
It is vector quantity. And its formula is v=s/t.
Its dimension and unit is [M0L1T-1] and m/s .
For a movable body is always positive, not zero or negative.
Instantaneous Velocity is a velocity at an instant of time (ds/dt).
Average Velocity is ratio of total displacement with total time interval.
Displacement-
Actual length between initial and final point.
It is vector quantity.
Its SI unit is meter and dimension is [M0L1T0].
For a moving body it can be positive, negative or zero.
Distance-
Total path length between initial and final point.
It is scalar quantity.
Its SI unit and dimension is meter and [M0L1T0].
For a moving body it always positive cannot be negative or zero.
Integration And Differentiation [Most Important] –
Integration is the mathematical operation to add very small segments.
It is denoted by symbol ∫x.d.x ,where ‘x’ is the function in terms of ‘t’.
Integration and differentiation both are reversible .
Integration Formula = n.xn-1
Differentiation Formula = [xn+1/x+1]
KINEMATIC EQUATION FOR UNIFORM ACCELETARION MOTION –
V = final Velocity , U= Initial Velocity , S or X = displacement , t = time a = acceleration .
There are derivation of 3 equation of motion by graphical method –
v = u + at –
BD/AC=acc.
a=(v-u)/t
at=v-u
v = u + at
(x) S = ut + 1/2at^2 –
x= area under triangle ABC + area of rectangle ACDO
X= [1/2 * AC * BC] + [AO * AD]
X=[1/2*t*(v-u)] + [u * t]
x=[1/2*(v-u)t] + [ut]
x=[1/2(at)t] + [ut] {v-u=at}
X=1/2at2 + ut
X=ut + 1/2at2
V2= u2 – 2as
X(S)=area of trapezium(ABDO)
X=1/2(v + u) * (t)
From v = u + at ,t = (v-u)/a
X=1/2(v + u) * (v-u)/a
X=1/2(v2 – u2)/a
2xa= v2 – u2
There are derivation of 3 equation of motion by calculus method –
v = u + at
S = ut + ½ at2
v2= u2 +2as
These all are the notes of chapter 2 in physics. And after some time you get important questions and NCERT solutions HERE. *#THANKS FOR VISITING, VISIT AGAIN#* 😊