How do I add velocity to particles?

I have a one-shot particle system that generates a cone of particles in a single blast at the player's position. If the player is moving, I would like the particles to either inherit the player's velocity or at least move with the player.

I've tried adding the particle system to the player object's hierarchy as well as manually moving the particle system, but this doesn't seem to affect the particles themselves.

Is there a simple way to do this?

My idea is that you create a variable of the player's speed, and that the particles follow that variable.