How to use something like SLERP but with continuous physics

Hey there. I am having a little trouble with my slerp function at the moment. When you hold down the X button on the controller you can zap a target towards you and when i reaches abotu 5 meters away from you it stops and you can then control the object around you in an arc by using SLERP and the controller joysticks.

The only issue i am having is that the physics are gone as soon as it enters the SLERP function. I have seen some pointers on the forums saying that because I am directly changing the objects position the physics are cancelling out. Is there any way to use something like SLERP for the arc type effect I am trying to achieve but with Physics attached?

Here is a quick diagram to illustrate what I am trying to do:

And here is my SLERP function: //controls the arc that the object is kept in void slerpFunc() {

         float damping = 2;
         //limits the Slerp function to the centre point of Roybot
         
         //sets up 3 vectors the start position and the end position for the interpolation
         //and the center point 
         Vector3 centre = transform.position;        
         Vector3 startPos = transform.position + new Vector3(0,0,5);
         Vector3 endPos = transform.position + new Vector3(0,0,-5);                
         centre -= Vector3.up;        
         Vector3 startRelCentre = startPos - centre;
         Vector3 endRelCentre = endPos - centre;
         
         //I am overriding the physics with transform.position. Need to find a better way to do this!!        
         target.transform.position = Vector3.Slerp(startRelCentre, endRelCentre, rightThumbValueY/damping);
         target.transform.position += centre;
     }

If anyone has come across this before or can help in any way it would be much appreciated!

Cheers :)