INSTRUCTOR WITH SPI IN A C172 TAXIES ONTO RWY WITH ANOTHER ACFT LNDG. UNABLE TAXI OFF IN TIME TO AVOID A COLLISION; HE TAKES OFF RAPIDLY.

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AFTER SOLOING A STUDENT AT JABARA ARPT IN WICHITA; KS; I HAD MY STUDENT GET OFF OF THE THIRD TXWY; WHICH IS APPROX 1/3 DOWN THE RWY FROM THE APCH END OF RWY 18. AFTER I GOT IN THE ACFT; I HAD MY STUDENT DO A 180 DEG TURN AND HEAD OUT TO DEPART RWY 18. I MADE A RADIO CALL; WHICH WAS FOLLOWED BY A RADIO CALL FROM AN ACFT ON FINAL. I LOOKED AND SAW NOTHING AND THEN PROCEEDED ONTO THE RWY. WHEN WE HAD ENTERED THE RWY I LOOKED AGAIN AND REALIZED THE ACFT ON FINAL WAS LNDG. IT WAS TOO LATE TO MAKE A 180 DEG TURN AND EXIT; SO I APPLIED FULL THROTTLE AND DEPARTED AS RAPIDLY AS POSSIBLE TO AVOID. THE ACFT NEVER CAME CLOSER THAN 300-500 FT TO EACH OTHER. FACTORS AFFECTING THE INCIDENT: 1) I WAS 15 MINS LATE FOR A CLASS AND IN A HURRY. 2) I HAD FLOWN 4 FLTS PREVIOUS TO THIS ONE AND WAS TIRED. 3) THE SLOPE OF THE RWY MAKES IT HARD TO SEE ACFT CLOSE TO THE GND FROM WHERE WE WERE ON THE RWY. IN SHORT; I HAD SEVERAL FACTORS PUSHING ME TO MAKE A RAPID DEP; AND MY DESIRE TO MAKE A RAPID DEP RESULTED IN A BAD DECISION TO DEPART WITHOUT HAVING CONFIRMED VISUAL SEPARATION WITH TFC. THIS RESULTED IN A NEAR COLLISION. I WILL MOST DEFINITELY BE MORE AWARE AND WARY OF IMPULSIVE HURRIED DECISIONS IN THE FUTURE.