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What you are asking about is called acceleration. Easing out and easing in. It is achieved by computing the elements current speed before you move it. The simplest way to do that if your goal is only smoothness in motion is to use acceleration. You do this like this (pseudo code): p.x = 10.0; // Current character position. v.x = 0; maxV.x = 1.0; // Inset ...


If you are looking to mimic old school platformers step one is to ditch physics altogether. You will end up fighting the physics system to get the decidedly non-realistic motion of an old school platformer. Have a look at this CharacterController replacement that ditches physics altogether to get a good idea of one way to implement it.

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