AFTER LOSING THE RETREAD CAP ON THE #1 TIRE; THE PIC OF A B737-300 FLT DECIDES TO CONTINUE THE FLT TO DEST ARPT AT MCI; MO.

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DURING TKOF FROM SLC; CAPT SUSPECTED BLOWN TIRE JUST PRIOR TO ROTATION. LNDG GEAR AND FLAPS WERE RETRACTED NORMALLY AND AFTER TKOF CHKLIST COMPLETED; CAPT THEN ASKED JUMP SEAT RIDER AND MYSELF IF WE NOTICED ANY UNUSUAL VIBRATIONS JUST PRIOR TO ROTATION -- WE HAD NOT. WE THEN CHKED WITH ATC. THEY CONFIRMED THAT PIECES OF TIRE WERE FOUND ON THE RWY WE USED. WE PROCEEDED ON COURSE; DISCUSSED OUR OPTIONS AND CONTACTED COMPANY DISPATCH AND MAINT CTL FOR GUIDANCE. EVERYONE CONCURRED WITH THE CAPT'S DECISION TO CONTINUE TO THE DEST (MCI) BECAUSE THERE WERE NO INDICATIONS OF ACFT DAMAGE (EXCEPT FOR THE FAILED TIRE); THE WX WAS EXCELLENT IN MCI; RWYS WERE LONG AND DRY AND THE 2 HR FLT WOULD BOTH BURN OFF FUEL FOR A LIGHTER LNDG WT AND ALLOW US PLENTY OF TIME TO DISCUSS ALL POSSIBLE CONTINGENCIES. IN HINDSIGHT; HAVING PLENTY OF TIME WAS VERY HELPFUL IN ALLOWING US TO CONSIDER ALL THE POSSIBILITIES; SOLICIT INPUT FROM VARIOUS SOURCES AND PREPARE OURSELVES TO THE MAX EXTENT POSSIBLE. THE CAPT ALSO USED THE ENRTE TIME TO BRIEF THE FLT ATTENDANTS ON THE SIT AND PLAN AS WELL AS ALLOW THEM TIME TO REVIEW EVAC PROCS. IN THE COCKPIT; WE REVIEWED EVAC AND PARTIAL GEAR EXTENDED LNDG PROCS. WE ALSO REQUESTED CFR ASSISTANCE AND PLANNED TO ROLL TO A TOP ON THE RWY; SHUT DOWN ENGS; AND BE TOWED TO THE GATE. THE CAPT FLEW A VISUAL APCH USING MAX FLAPS (40 DEGS) TO MINIMIZE TOUCHDOWN SPD AND BRAKING. HE BRIEFED THE USE OF MINIMAL BRAKING AND REVERSE THRUST TO INSURE DIRECTIONAL CTL AND MINIMIZE THE CHANCE OF FOD TO THE ENG(S). LNDG L OF CTRLINE WAS DISCUSSED (AS CAPT 'FELT' IT WAS THE R SIDE TIRE(S) THAT FAILED); BUT LATER DISMISSED BECAUSE WE HAD NO DEFINITIVE EVIDENCE OF WHICH SIDE FAILED. (IT TURNED OUT THE L #1 TIRE FAILED.) NORMAL APCH; LNDG AND ROLLOUT WERE MADE. POSTFLT INSPECTION REVEALED #1 TIRE TREAD SEPARATION WITH REMAINING #1 TIRE INTACT; DAMAGE TO L LNDG GEAR DOOR AND TRAILING EDGE FLAP DAMAGE. SUPPLEMENTAL INFO FROM ACN 523621: LNDG WAS UNEVENTFUL EXCEPT FOR CONTINUOUS VIBRATION DURING ROLLOUT. OUR MAINT CHKED THE ACFT. THE GEAR WERE PINNED AND THE ACFT WAS TOWED TO THE GATE.