wave particle duality - Difficulties in understanding basic energy equation in quantum mechanics

While reading a text book about basics of Quantum Mechanics, I came across a situation in which it is said that

$E=\hbar\omega$ and also

$E = \frac12mv^2=p^2/2m$

where

$h$ Planck's constant

$\hbar=\frac{h}{2\pi}$ Planck's reduced constant

$\omega=2\pi f$ angular frequency

$m$ mass

$v$ velocity

$p$ momentum

But if I take the first definition,E=(h/2pi)*w,then

E=(h/2pi)*2*pi*f (because w=2*pi*f)


 = h*f

 = h*(v/λ)       (because v=fλ)

 = p*v           (de-Broglie's wave-particle duality p=h/λ )

 = mv*v          (because p=m*v, the momentum)

E = m*v^2

This is not same as definition $E=\frac12mv^2$.

What am I missing in the derivation above?