May be right. But what I had observed one more thing that the source mesh is having only 10 vertices.So I need to pull only those two right vertices of the box on the X axis.The current logic of the apply() method is updating all vertices and applying to all vertices of destination mesh.But from the vertices list of he source mesh, can I know which are those two right vertices of the box that are to be stretched? .Please correct me.

@EgonOlsen. Thanks.It really helped. .I know my level of understanding is very little here.Now it works.

That is ok ...@EgonOlsen.No probs.. .
But even if I commented that line , what happens is that the box size is not getting affected on x-axis when I press some key.Can I extend a box on its x-axis so that the box slowly turns to be a 3d rectangle?

I resolved this error by commenting the constructor call in the VertexController.This is the modified code.
      class VertexController extends GenericVertexController {

        public VertexController( Object3D toCheck ) {
     // super.init(toCheck.getMesh(), true);
        }
        public void apply() {
            SimpleVector[] vertices   = getSourceMesh();
    SimpleVector[] destination = getDestinationMesh();
            for (int i = 0; i < vertices.length; i++){
             vertices[i].x *= vertices[i].x * 5;
     destination[i].x = vertices[i].x;
    }
   //this.updateMesh();
        }
      }
===================
        public boolean onKeyDown(int keyCode, KeyEvent msg) {
          if( keyCode == KeyEvent.KEYCODE_A ) {
              System.out.println(" total angle swept " + box.getTransformedCenter().calcAngle(box.getXAxis()) );
              //world.removeObject(box);
              //box = createBox(xDelta, 0.75f);
              //box.setAdditionalColor(RGBColor.WHITE);
              //box.translate(-10, 10, 0);
              //world.addObject( box );
              //world.buildAllObjects();
              VertexController vc = new VertexController(box);
              Mesh mesh = box.getMesh();
              mesh.setVertexController(vc, true);
              mesh.applyVertexController();
              xDelta+=1.5f;
              return true;
          }
         return true;
        }

After making these changes , I am able to run the application. But when  I press the A key, the box size is not increasing on x-axis.Is there anything I missed here?

what exactly the strip() method tries to do here?

Let me try that

one more clarification,I have a box.As per the above pic, if I place one more box next to previous one, then what I need to do is share the vertices of the previous box.Then I think, the placing issues can be resolved.This is what @EgonOlsen has suggested.But using API , I do not know how to do it.