Smooth Lerp movement?

Currently it just teleports the player to the position of the empty object. How can i make it smoothly move to the empty object?

var touchingLedge : boolean;
var player : GameObject;
var end : Transform;
var start : Transform;

function Update () {

	if (touchingLedge == true)
		player.transform.position = Vector3.Lerp(start.position, end.position, Time.time);
		
}

function OnTriggerEnter (hit : Collider)
{
 if (hit.gameObject.tag == "Player")
 	touchingLedge = true;
 	yield WaitForSeconds(0.3);
 	touchingLedge = false;

}

Here’s a solution I ran across some time ago, likely from these boards. Lerp over time. I think it will work as you want it to:

//Declared somewhere near touchingLedge
var moving : boolean = false;

function Update () {
	if (touchingLedge == true) {
		//Last variable is seconds you want Lerp to last
		StartCoroutine(MoveFromTo(start.position, end.position, 0.5f));
	}
}

function MoveFromTo(pointA : Vector3, pointB : Vector3, time : float) {
	if (!moving) { 					// Do nothing if already moving
		moving = true; 				// Set flag to true
		var t : float = 0f;
		while (t < 1.0f) {
			t += Time.deltaTime / time; // Sweeps from 0 to 1 in time seconds
			transform.position = Vector3.Lerp(pointA, pointB, t); // Set position proportional to t
			yield; 		// Leave the routine and return here in the next frame
		}
		moving = false; 			// Finished moving
	}
}