I DROVE THE VEHICLE [XXX] ABOUT 25 MILES FROM HOME TO A DOCTOR'S OFFICE, AT TYPICAL NORTHERN VIRGINIA HIGHWAY SPEEDS ON I-66 & I-495. I ARRIVED AT THE DOCTOR'S OFFICE, I ENTERED THE PARKING LOT AT ABOUT 5 MPH, I APPROACHED A PARKING SPACE AND AT ABOUT 2 MPH MADE A RIGHT-TURN INTO THE SPACE. WITHOUT WARNING, THE VEHICLE STARTED ACCELERATING. I COULD NOT STOP IT EVEN WITH BOTH FEET ON THE BRAKE PEDAL. THE VEHICLE JUMPED OVER A CONCRETE PARKING STRIP, THEN THE CONCRETE CURB, UP A SLIGHT EMBANKMENT AND THROUGH A WOODEN FENCE. THE VEHICLE EVENTUALLY CAME TO REST WITH 3 OF THE 4 TIRES ON THE EMBANKMENT OVER THE CURB. THE RIGHT-REAR TIRE WAS RESTING AGAINST THE PARKING CURB STRIP. THE VEHICLE CONTINUED TO LURCH FORWARD TRYING TO PULL THE LAST WHEEL UP OUT OF ITS RESTING SPOT. I LOOKED DOWN AT THE BRAKE/ACCELERATOR PEDALS AND THOUGH BOTH OF MY FEET WERE ON THE BRAKE PEDAL, THE VEHICLE WAS STILL TRYING TO MOVE FORWARD. I SHIFTED THE VEHICLE INTO PARK AND THE VEHICLE CONTINUED TO TRY TO LURCH FORWARD, SO I TURNED OFF THE ENGINE. AFTER DEPARTING THE VEHICLE, I CHECKED THE DRIVER'S SIDE FLOOR MAT AND NOTED THAT THE FLOOR MAT WAS PROPERLY POSITIONED, HOOKED TO HOOKS ON THE FLOOR OF THE VEHICLE. THE CAR WAS TOWED TO A LEXUS DEALERSHIP WHERE IT WAS INSPECTED BY A TOYOTA-AUTHORIZED ENGINEER. SINCE THE EVENT COULD NOT BE REPRODUCED, WE WERE TOLD THAT THERE WAS NOTHING WRONG WITH THE VEHICLE AND THAT IT WAS SAFE TO DRIVE. THOUGH WE WERE TOLD THAT WE WOULD BE PROVIDED WITH THE ANALYSIS OF