Lerp can someone explain please

You have a couple options, some not built into unity:

First, Ill explain how lerp works: Ill use Mathf.lerp for ease of understanding This is what Lerp basicly does internaly

SUDO CODE:

 float Mathf.lerp(float from, float to,float percent){
   differnce =  to - from;
   return = from + (differance*percent);
 }

So in otherwords, If you feed in 0.10 or 10% Lerp will move the from 10% closer to the to; so the thing to remember is the distance it moves gets smaller and small... IE: Lerp(100,0,0.1) = 90 , Lerp(90,0,.1) = 81 , Lerp(81,0,.1) = 72.9 , etc , etc

You may want to use Vector3.movetowards or Mathf.moveTowards you put in a from, and to positions, but instead of a % along path, it will never move faster than the speed you feed into it;

finanaly if you need a different solution such as smooth out, and smooth in. You may want to check out iTween : http://itween.pixelplacement.com/index.php

you also said:

There is NOT a lot of info on this subject, and the game engine doesn't recognize algebraic functions that dictate velocity over time.

Also, to address this, You have to build you velocity over time around the update loop, meaning, you ether need to track time yourself using Time.time or Time.deltaTime or System.DataTime.Now

IE:

 public Vector3 myWorldVelecoity = new Vector3(10,0,0); //Move along the world X at 10 units per second                
 public void Update(){
     this.transform.Translate(myWorldVelecoity * Time.deltaTime);
     // OR
     this.transform.position = this.transform.position + (myWorldVelecoity * Time.deltaTime);
 }