(3-6A)

Start from the definition of work:   W  = FΔx

Now use the equation of motion to substitute in an expression for Δx:

v2 = u2 + 2aΔx so:

Δx  =  (v2 - u2) / 2a and hence,:

W  = FΔx  =  F(v2 - u2) / 2a

Now, Newton's second law tells us that a = F/m,   so let's make this substitution into the work expression:

W  =  F(v2 - u2) / 2(F/m)    =   m(v2 - u2) / 2   =   mv2/2  - mu2/ 2

which is the change in kinetic energy as the velocity changes from u to v. 

QED (as they say).