FIRST
EQUATION OF MOTION
Vf = Vi + at
|
|
| Consider
a body initial moving with velocity "Vi". After certain interval
of time "t", its velocity becomes "Vf". Now
|
Change
in velocity = Vf - Vi
OR
DV
=Vf – Vi
|
|
Due
to change in velocity, an acceleration "a" is produced in the
body. Acceleration is given by |
|
a
= DV/t
|
| |
Putting
the value of "DV" |
|
a
= (Vf – Vi)/t
at = Vf – Vi
at + Vi =Vf
OR
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SECOND EQUATION OF MOTION
OR
S = Vit + 1/2at2
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|
Consider a car moving on a straight road with an initial velocity equal
to ‘Vi’. After an interval of time ‘t’ its velocity becomes ‘Vf’.
Now first we will determine the average velocity of body.
|
Average
velocity = (Initial velocity + final velocity)/2
OR
Vav = (Vi + Vf)/2
|
| but
Vf = Vi + at |
| Putting
the value of Vf |
Vav
= (Vi + Vi + at)/2
Vav = (2Vi + at)/2
Vav = 2Vi/2 + at/2
Vav = Vi + at/2
Vav
= Vi + 1/2at.......................................(i)
|
| we
know that |
S
= Vav x
t
|
| Putting
the value of ‘Vav’ |
S
= [Vi
+ 1/2at]
t
|
|
|
THIRD
EQUATION OF MOTION
OR
2aS = Vf2 – Vi2
|
|
| Initial
velocity, final velocity, acceleration, and distance are related in third
equation of motion. |
Consider
a body moving initially with velocity ‘Vi’. After certain interval
of time its velocity becomes ‘Vf’. Due to change in velocity,
acceleration ‘a’ is produced in the body. Let the body travels a distance
of ‘s’ meters.
According to first equation of motion: |
Vf
= Vi + at
OR
Vf – Vi = at
OR
(Vf
– Vi)/a = t....................(i)
|
| Average
velocity of body is given by: |
Vav
= (Initial velocity + Final velocity)/2
Vav
= (Vi + Vf)/2..................
(ii)
|
| we
know that : |
S
= Vav x
t.................. (ii)
|
| Putting
the value of Vav and t from equation (i) and (ii)
in equation (iii) |
S = { (Vf + Vi)/2}
{
(Vf – Vi)/a}
2aS = (Vf + Vi)(Vf – Vi)
|
| According
to [
(a+b)(a-b)=a2-b2] |
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