a forced sliding animation with EaseIn at the end in flutter

I am trying to create an animation that is triggered with a slide.

So I have a normal page that is decided in two, one part has the same height as the screen and is show at first as if you only have that part. the second part needs to slide up. my idea is to make the sliding responsiveness harder like you need to move your finger for much longer distance to have a good sized part of the bottom part of the page show up.

this way the user needs to really intent on sliding, and once that intent has been verified I want the slide to just easeIn on itself and finish the sliding animation automatically on its own.

I tried looking for a name or an animated bit showing this but failed, does anyone know how to do this in flutter ?