PVT PLT DURING COMPLEX ACFT TRAINING BLEW A MAIN GEAR TIRE DURING LNDG ROLL OUT DUE TO EXCESSIVE BRAKING.

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WE WERE CLRED TO LAND BY THE TWR FROM ABOUT A 5 MI L BASE TO RWY 18. I BELIEVE THE WIND WAS APPROX 240 DEGS AT 12 GUST 22. THE APCH ON FINAL WAS UNEVENTFUL. THE PVT PLT (THIS WAS HIS ACFT) WAS VERY CAPABLE IN GUST CONDITIONS AND SHOWED GOOD XWIND PROFICIENCY BY INCREASING HIS APCH SPD TO COMPENSATE FOR THE GUSTY WINDS. HIS TOUCHDOWN AND INITIAL ROLLOUT WERE TEXTBOOK PERFECT AT WHICH TIME THE TWR CTLR INFORMED US THAT THERE WAS 'A LEAR JET ON SHORT FINAL AND FOR US TO MAKE A TURN ON THE NEXT TXWY (L).' THIS IS WHERE MY STUDENT SHOWED POOR JUDGEMENT BY GETTING HARD ON THE BRAKES DESPITE THE FACT THAT WE WERE GOING TOO FAST TO MAKE THE TURN. MY REACTION WAS TO RETRACT THE FLAPS. THE L TIRE BLEW OUT AND WE ROLLED TO A STOP WITH THE L MAIN JUST OFF THE RWY. I IMMEDIATELY RADIOED THE TWR AND INFORMED HER WE WERE DISABLED AND SHE SENT THE ACFT ON FINAL AROUND. CAUSE OF THE TIRE BLOWOUT: EXCESSIVE BRAKING; SIDE LOAD FROM XWIND. CONTRIBUTING FACTORS: TWR AND APCH CTL NOT ALLOWING SUFFICIENT SEPARATION FOR CONDITIONS. PLTS OF LEARJET WERE ASKED TO SLOW DOWN SEVERAL MI OUT; BUT APPARENTLY DIDN'T SLOW ENOUGH. I DO NOT KNOW EXACTLY HOW FAR BEHIND US THE LEARJET WAS; BUT THE TWR CTLR'S VOICE MADE IT SOUND URGENT THAT WE TURN AT TXWY L. 200 HR PVT PLT MORE WORRIED ABOUT MAKING TURN TO APPEASE THE TWR THAN CTLING THE ACFT. INSTRUCTOR (ME) NOT SEEING THE SIT COMING.