How Do You Calculate Group and Phase Velocities in Wave Motion?

[Nusc]

Suppose you have this energy density A*cos^2(wt-kx+delta)

If you want find the velocity of this, I would suppose you would utilize the kinetic energy ?

What is the formula in this case?

 

[Matterwave]

Since that energy density has $k$ and $\omega$ in it, I presume you know those parameters. In such a case, you can find the group and phase velocities in the following manner (I'm guessing this is a 1-D problem due to lack of vector symbols in your post):

$$v_{gr}=\frac{\partial \omega}{\partial k}$$
$$v_{ph}=\frac{\omega}{k}$$