**derive third equation of motion**

Q1- Establish the relation v^{2} – u^{2} = 2as, where ‘u’ is the initial velocity, ‘v’ the final velocity, ‘a’ the uniform acceleration and ‘s’ is the distance covered by the body.

**Third equation of motion** – Let a body start with initial velocity u and after covering distance s under uniform acceleration a, its velocity becomes u in t seconds. Then

Average velocity =**(u+v)/2**

So the distance covered in time t is given by

s = Average velocity x Time =**[u +vxt]/2**

**v+u =2s/**t …….(i)

Using the first equation of motion : v = u + at

or **v-u=at ** …….(ii)

Multiplying equations (i) and (ii), we get**(v + u) (v – u)= (2s x at)/t**

or

**v ^{2} – u^{2} = 2as**

derive third equation of motion,derive third equation of motion

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