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How to make sprite move in the direction it's facing?

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Nope, pixi just draws stuff really really fast! Actually it does interactive stuff too but thats by-and-by.

I can vouch for P2 and also matterJS, both allow any rendering front-end to be bolted on (not all physics libraries do, some like to be tied to the rendering, which, in my opinion is plain wrong, do one thing well), in my experience P2 was easier to integrate, its a very powerful package. Both libraries have a pixi example in their source repos.

You should be able to find examples of bolting either physics lib and pixi together, or if you know phaser then phaser packages P2 if you dont mind using slightly older versions.

If you want to roll your own though, a simplified physics library just to help you move stuff around, its not too difficult (if you know your maths a bit) and a good exercise. The physics only gets hard when you want a fairly realistic simulation, stuff like collisions and everything can get hairy, just moving around isn't too difficult.

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