# What is Third Equation of Motion

## 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

=> a= Vf – Vi

Or

t = (Vf – Vi)/a ——–(i)

Substituting the average velocity

Vav = (Vi + Vf)/ 2 ————–(ii)

We know that:

Vav = S/t

S = Vav * t

Putting the value of Vav from equation (ii) and value of t from eq (i):

S = [(Vi + Vf)/2] * [(Vf-Vi)/a]

S = Vi2 – Vf2/2a since {(a+b) (a-b) = a2 – b2}

Or

2as = Vf2 – Vi2

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