I think I did the necessary changes but it got worse. The cue ball is moving in different directions, sometimes it stops and starts moving in a random direction.

    public boolean travel(double dt) {

        if (!ballMoved)
            return false;
        //for a 2D space the velocity operations is treated as a vector
        double velocity = Math.sqrt(vx * vx + vy * vy);
       
        //BACKUP the previous velocity value
        double vxs = vx;
        double vys = vy;
       
        if (velocity != 0. && !inHole)
        {
            dxx = vx / velocity;
            dyy = vy / velocity;
            velocity -= a * dt;
           
            if (velocity < 0.)
            {
                vx = 0.;
                vy = 0.;
            }
            else
            {
              /* Average Velocity = Displacement / Change in time
                OR  (x2 - x1)/ (t2 - t1)
              */
              //CALCULATE THE NEW VELOCITY
              //before it was vx = velocity * dxx;// vy = velocity * dyy;
                vx -= a * dt;
                vy -= a * dt;
            }
        }
        //CALCULATE THE DISPLACEMENT
        //before it was x += vx * dt;  y += vy * dt;
        x += (vxs+vx) * dt/2; //add value to the x coordinate
        y += (vys+vy) * dt/2; // add value to the y coordinate
       
        if(isWithinLimits(x, y))
          { /*no action taken*/ }
        else if(inHole)
          {
                vx = 0.;
                vy = 0.;
          }
        //if the x and y coordinate value are larger than the limits
        //which are the table boundary
        else
            changeDirection();