Calculate needed y velocity for given y point

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In my mobile game, the main character needs to jump to a specific y point before starting to fall down again due to gravity. How could I calculate the y velocity I would need to reach (at peak) a given y position with a given gravity? 

I tried to do this with a tween instead of arcade physics because it was exactly what I needed (distance traveled over time with a gravity-like effect), but the performance was not good and was constantly sputtering.

I'm currently using Phaser 2.6.2. Thanks!

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