A C172 TRAINING FLT ON ROLLOUT FOR A TOUCH-AND-GO IS FACED WITH OPPOSITE DIRECTION TFC ON APCH FOR LNDG ON OCCUPIED RWY 31 AT SGJ; FL.

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SGJ HAS RECENTLY CHANGED UNICOM/CTAF FREQ FROM 122.2 TO 127.625. MY FLT INSTRUCTOR AND I ENTERED THE TFC PATTERN NORMALLY; COMMUNICATING OUR INTENTIONS ALONG THE WAY ON 127.625. THERE WERE SEVERAL OTHER ACFT IN THE PATTERN FOR RWY 31 AS WELL. WE WERE TO DO A TOUCH-AND-GO; SO WE LANDED NORMALLY; RECONFIGURED FOR A NORMAL TKOF AND APPLIED FULL PWR. AT THIS POINT; I SAW THE ACFT AT THE END OF THE RWY (RWY 31) THAT APPEARED TO BE LNDG ON RWY 13; SO I ABORTED TKOF AND STEPPED ON THE BRAKES HARD TO SLOW THE ACFT AND GET OFF THE RWY. MY INSTRUCTOR COMMUNICATED ON 127.625 THAT THE ACFT ON FINAL WAS LNDG ON AN OCCUPIED RWY. THE ACFT DID NOT RESPOND. MY INSTRUCTOR THEN TURNED TO 122.80 AND REXMITTED. THE OTHER ACFT THEN DID A MISSED APCH. MY INSTRUCTOR THEN INFORMED HIM OF THE FREQ CHANGE AND ALSO TOLD HIM TO BE SURE TO CHK THE NOTAMS BEFORE FLT. THE OTHER PLT APOLOGIZED; NOTED THE FREQ CHANGE AND TOLD US THAT HE SAW US ONLY AFTER WE HAD SMOKED THE TIRES TRYING TO SLOW DOWN. AS IT TURNS OUT; THE TIRE WAS SO FLATTENED ON ONE SIDE THAT IT HAD TO BE REPLACED. UPON OUR RETURN TO CRG; THE OTHER ACFT RE-ENTERED THE PATTERN FOR RWY 31; COMMUNICATING HIS INTENTIONS; DID 1 TOUCH-AND-GO AND DEPARTED TO THE N. WE TAXIED BACK TO RWY 31; TOOK OFF TO THE N FOR MORE TRAINING.