EQUATIONS OF MOTION EQUATIONS OF MOTION
 
 
 
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
SECOND EQUATION OF MOTION
OR
S = Vit + 1/2at2
 
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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