Work energy theorem

work energy thereom for kinetic energy is :
we know that 
v²-u²=2as;
multiply both sides with m/2 then we get 
(mv²-mu²)/2=mas
we know that 
1/2mv^​2&1/2mu²=kinetic energy (final&intial ) respectively & ma=F(product of mass &acceleraiton is  force(from newton 2^ndlaw)
therefore 
1/2mv^​2-1/2mu²=F.S
K_f- - K_i=F.S
we know that F.S= W(force vector dot displacement vector =work done )
therefore total work done =change in their kinetic Energy