EQUATIONS
OF MOTION EQUATIONS OF MOTION


FIRST
EQUATION OF MOTION
V_{f} = V_{i} + at 

Consider a body initial moving with velocity "Vi". After certain interval of time "t", its velocity becomes "V_{f}". Now  
Change
in velocity = V_{f}  V_{i}
OR DV =V_{f} – V_{i} 


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 = V_{f} – V_{i} at + V_{i} =V_{f} OR 

SECOND EQUATION OF MOTION
OR S = Vit + 1/2at^{2} 

Consider a car moving on a straight road with an initial velocity equal to ‘V_{i}’. After an interval of time ‘t’ its velocity becomes ‘V_{f}’. Now first we will determine the average velocity of body.  
Average
velocity = (Initial velocity + final velocity)/2
OR V_{av }= (V_{i} + V_{f})/2 

but V_{f} = V_{i} + at  
Putting the value of Vf  
V_{av
}= (V_{i} + V_{i }+ at)/2
V_{av }=_{ }(2V_{i }+ at)/2 V_{av} = 2V_{i}/2 + at/2 Vav = V_{i }+ at/2 V_{av} = V_{i }+ 1/2at.......................................(i) 

we know that  
S
= V_{av}_{ }x
t


Putting the value of ‘V_{av}’  
S
= [V_{i
}+ 1/2at]
t




THIRD
EQUATION OF MOTION
OR 2aS = V_{f}^{2} – V_{i}^{2} 

Initial velocity, final velocity, acceleration, and distance are related in third equation of motion.  
Consider
a body moving initially with velocity ‘V_{i}’. After certain interval
of time its velocity becomes ‘V_{f}’. 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: 

V_{f}
= V_{i} + at
OR V_{f }– V_{i }= at OR (V_{f} – V_{i})/a = t....................(i) 

Average velocity of body is given by:  
V_{av}
= (Initial velocity + Final velocity)/2
V_{av }= (V_{i} + V_{f})/2.................. (ii) 

we know that :  
S
= V_{av} x
t.................. (ii)


Putting the value of V_{av }and t from equation (i) and (ii) in equation (iii) 

S = { (V_{f }+ V_{i})/2}
{
(V_{f }– V_{i})/a}
2aS = (V_{f }+ V_{i})(V_{f }– V_{i}) 

According to [ (a+b)(ab)=a^{2}b^{2]}  


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