A C150 HAS AN ENG FAILURE AFTER TKOF RESULTING IN LNDG JUST SHORT OF THE RWY.

Narrative

I WAS ON AN INSTRUCTIONAL FLT WITH A STUDENT AND UPON RETURNING TO THE ARPT; WE PLANNED TO DO A TOUCH AND GO FOLLOWED BY A FULL STOP. THE STUDENT WAS IN CTL WHILE TAKING OFF FROM THE TOUCH AND GO WHEN I NOTICED A HESITATION IN THE ENG. I IMMEDIATELY TOOK CTL OF THE ACFT AND ANNOUNCED 'MY CTLS.' STUDENT RELINQUISHED CTLS AND I THINK; ASSUMED HE HAD DONE SOMETHING WRONG. I IMMEDIATELY THEREAFTER; ADDED FULL MIXTURE AND TURNED ON CARB HEAT WHICH INITIALLY SEEMED TO WORK AND PWR WAS RESTORED. BASED ON THE FACT THAT I THOUGHT PWR WAS RESTORED I CALLED TWR; NOTIFIED THEM I HAD ENG TROUBLE AND TURNED R ONTO XWIND FOR RWY 24R. TWR CLRED ME TO LAND ANYWHERE NECESSARY AND I ADVISED THEM I WOULD LAND RWY 15. I WAS CLRED TO LAND RWY 15. WHILE TURNING FROM WHAT WAS (R) XWIND FOR RWY 24R TO WHAT WAS NOW R BASE FOR RWY 15 THE ENG AGAIN QUIT; THIS TIME COMPLETELY. I PITCHED FOR BEST GLIDE AND PREPARED MY STUDENT FOR AN EMER LNDG. I THINK MY STUDENT WAS UNAWARE FOR THE MOST PART THAT THIS WAS AN ACTUAL EMER AND NOT A TRAINING EXERCISE. THE PLANE LANDED JUST SHORT OF THE RWY AND CAME TO A STOP ON THE RWY. NEITHER MYSELF; THE STUDENT; THE PLANE; OR ANYTHING ELSE SUFFERED ANY DAMAGE. THE PLANE WAS THEN TOWED TO THE HANGAR AND WAS STARTED UP BY THE MECH. THE PROB COULD HAVE BEEN CARB ICE; AS IT WAS AN UNUSUALLY HUMID DAY FOR ARIZONA. THE LOW FUEL QUANTITY ALSO COULD HAVE BEEN A FACTOR WHICH IS WHAT I SUSPECT. THE CESSNA 150 HAS SMALL TANKS AND MAY HAVE HAD INTERRUPTION OF FUEL FLOW EITHER DUE TO MOISTURE OR SLOSHING OF FUEL. I LATER DISCUSSED THE EVENTS WITH MY STUDENT AND EXPLAINED THAT ALTHOUGH THINGS TURNED OUT; A BETTER CHOICE MAY HAVE BEEN TO SELECT A LNDG AREA STRAIGHT AHEAD.