Question: how to start slow, and then increase in speed based on distance.

My question is as above. How do I move an object starting slow and increasing the speed based on the distance to the target object?
I'm using a mouseposition object for the target.
I've tried using Vector3.Lerp but it only has a set speed at which it moves the desired object.
I think i want a custom function like lerp but better, only I don't know how to make one.

 

I can provide an example too by the way. this flash game alpha bounty uses the sort of function I'm talking about in it's move to mouse position code. https://kbhgames.com/game/alpha-bounty

 

Vector3.SmoothDamp does exactly what you want.

 

Thankyou that is exactly what i was looking for.