How can I move object as natural?

I want to move the cube object to the left if I touched right side of half of the screen.
The other way, move the cube object to the right if I touched left side.
And the object have to move natural.
Of course, if touched again the object have to accelerated when the object is still moving. (I think this can be used by Physics)
In short, I want to make ballon effect.

In this case, which approach is more effective?
I used LeanTween, iTween to move object. But when I fast double touched, it doesn’t move natural.
And Physics is not yet studied.

Is there a good way to implement that effect…?
Help me!

I think you’re gonna need to use the (or any) Physics engine if you want a fluid, natural movement.

Start here, if you’re not sure how to proceed:

http://unity3d.com/learn/tutorials/modules/beginner/physics