To prove: 
 v^2 =u^2 + 2as
we have,
 a = v-u/t
 or, t= v- u/a......(i)
Again,
 s = u + v /2*t...........( ii )
Substitutung the value of 't' from equation (i) in equation ( ii ) , we have,
 s= (u+v/2) * ( v- u/a)
 or, s=(v^2 - u^2) /2a
 or, 2as = v^2 - u^2
 therefore, 
 v^2= u^2 + 2as
 proved...
   hope this helps!!!!