# How to show speed is equal to group velocity?

## Homework Statement

My question is, how do I show that speed is equal to group velocity? More information at https://imgur.com/a/m6FwNaG

v_g = dw/dk

## The Attempt at a Solution

Part a is substitution, part b uses v_g = dw/dk, part c is multiplication by h-bar, but I am stuck at part d. We are dealing with a relativistic energy equation, but the question says "the speed v" as if that has some meaning. What am I missing? I have a feeling I am overlooking something incredibly simple.

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RPinPA
The speed v is the speed that occurs in the relativistic factor $\gamma = 1/\sqrt {1 - (v^2/c^2)}$. And momentum depends on velocity, $p = \gamma mv$. So it looks like you need to solve for the momentum, and from that solve for the velocity.
Edit: I realized on thinking about this that it would be even easier to simply use the fact that $E = \gamma mc^2$ and solve for $\gamma$ and v that way.