DURING CLB MLB RECEIVES TCASII RA TO DSND. UNABLE TO STOP CLB PROMPTLY.

Narrative

WX WAS CLR. WE WERE TAKING OFF ON RWY 9L; CLBING TO 5000 FT. AT 2000 FT; WE WERE CLRED TO 10000 FT. WE WERE ON RWY HDG. AT ABOUT 5000 FT WE TURNED TO A HDG OF 360 DEGS. MY CLB RATE WAS ABOUT 2000-3000 FPM. AT 7000 FT WE GOT A TCASII WARNING. IT WAS RIGHT IN THE CTR OF THE SCREEN. WITHIN SECONDS; THE TCASII TOLD US TO DSND. BEFORE THIS POINT; I HAD ALREADY STARTED TO PWR BACK AND NOSE THE PLANE OVER. ATC HAD SAID NOTHING UP TO THIS POINT. BTWN THE 2 TCASII WARNINGS; WE ASKED IF THEY HAD THE TFC. THINGS WERE HAPPENING VERY QUICKLY AT THIS POINT; AND I BELIEVE ATC SAID THEY DID NOT HAVE THE TFC. THE TFC WAS AT 8000 FT. BY THE TIME WE GOT THE WARNING; SPOKE TO ATC; THEN FINALLY SAW THE TFC; I HAD CLBED TO 8500 FT. AT THIS POINT ATC SAYS TO LEVEL AT 8000 FT. I STARTED SLOWLY BACK TOWARD 8000 FT. NOW THAT WE HAD THE TFC IN SIGHT WE ASKED ATC TO CONTINUE CLB TO 10000 FT. THE TFC WAS CLRLY AT 8000 FT; FLYING WBOUND; RIGHT OVER PHL INTL. WE DID WHAT WE WERE SUPPOSED TO DO. I WISH ATC HAD NOTICED THE ACFT SOONER. ATC SHOULD BE MADE AWARE THAT JET ACFT CANNOT STOP CLBING ON A DIME. AT BEST; YOU MIGHT BE ABLE TO LEVEL IN 500 FT; BUT NOT VERY SMOOTHLY. OVERALL; I AM GLAD THE TCASII SYS WORKED SO WELL.