I'm designing a game where characters' speed starts slowing down after different distances. I'm not advanced in mathematics so I'm not sure if I'm on the right track. After researching on wikipedia I found information on Gompertz function and Sigmoid function. My primary question is if one of these are the formula I need or is there a simpler way to describe what a characters speed will be?
To be specific: The max speed a character can have is $32$m/s, the minimum is $16$m/s. The most unfit character starts to slow down immediately from $32$m/s to $16$m/s in $16$ seconds. The most fit character doesn't start slowing down until after $16$ seconds. The variable of when the slow-down begins can fall anywhere between $0$s and $16$s of travel. Would be awesome if someone could show what the formula would look like for this.