Simple equation for simulating different acceleration curves?

Question

For a video game, I would like to simulate different acceleration curves for different types of cars.

I found out about Logistic and Sigmoid functions and while interesting they produce a symmetrical result:

I'm looking for something asymmetrical, like one car that accelerates quickly, another car that accelerates slowly and so on. (shown in red)

For my input, it will be linear from 0.0 to 1.0, as long as joystick button is held down, I increment X. (shown in black)

Can you suggest a simple equation that would allow me to generate such kind of curves by tweaking a few parameters?

Answer 1

Maybe B-Splines are of interest to you.