Hi, I have a little problem with functions and curves. When it comes to statistics, functions and curves I'm a really noob, so I hope this is the right forum.

Some background information: I'm developing a game where objects move across the y-axis according to the passed time. These objects are stored in a 2d matrix. If I move them by one position in the matrix, the objects would "jump" from y(5) to y(6) but I want fluent animation between y(5) and y(6).

So I have created this function:y = (S / D⋅x) - S

S and D are two constants: The size of the moving object and the duration of one gamestep in ms.

x describes the passed time.

I've decreased by S because I needed the result to be negative to zero.

The object moves fluently but this is not exactly what I wanted. I want the movement between two matrix positions start rather slowly (nearly stop at the begin) and get very fast to the end. This way the user can better distinguish if the block is actually at y(5) or y(6) and also get the illusion of fluent animation.

This image should make it clearer: (S = 25; D = 100)

The black line is what I have now. The red line is what I would like to have (or similar).

As I already said I'm really bad at such things, so I hope someone can help me with that problem.

Thanks in advance!