Explain why atoms move at different speeds depending on whether that are in liquids or solids

Turn it around and you'll have it.

The atom doesn't say "Oh gosh, I'm in a liquid now,
I'll have to move faster."

When the atoms have generally low energy, that means they're 
moving relatively slowly ... just kind of jiggling in place but not
going on any long trips ... and you have a solid.

If you GIVE the atoms more energy, that means now they're
moving faster, and are able to move away from their places
and flow like a liquid.

And if you give them even MORE energy and make them move
even faster, then they're free to shoot around wherever they want,
the liquid evaporates, and they form a gas. 

They don't move fast because they're in a gas.
They form a gas because they're moving fast.