Driving on a 4 lane street at approximately 25 mph in the right hand lane next to curb when another vehicle swerved from the left lane into my lane. I slammed on the brakes in an attempt to stop and avoid any contact with the other vehicle. All the brakes did was a hard and long shudder, and did not seem to even slow my car let alone stop the car. Fortunately, the other vehicle attempting to swerve into my lane stopped. My vehicle never stopped and only seemed to slow down slightly. All I could do was to move my vehicle more towards the curb. At the time, I did not feel any impact and assumed no contact or damage. The other driver continued down the road and got onto the highway. When I got to a place to stop, I looked at my vehicle and do have damage to the left rear wheel well trim and back quarter fender area. My car would not stop. It felt as the ABS system was modulating hard. The road was dry, and the temp was in the mid 60's. This is not the first issue like this, and Hyundai says there is no problem and they will not fix it. The last time I took into the shop for this, it was there almost 90 days before Hyundai said come get the vehicle.