Nikon calls it FP sync mode or Auto FP, but I don't think the D3000 has that feature, but the SB-600 certainly does.
Look in your users manual index (the one of the white disc), for FP sync mode. (flash modes starts on page 59. Optional flash unit info starts on page 162, but I don't see anything about FP sync mode. As always familiarity with your users manual is always helpful.)
The camera shutter is made of 2 curtains. Nikon calls them the front and rear curtains.
The front curtain drops exposing the image sensor and then the rear custain drop scovering the image sensor back up. They both then reset to the top for the next exposure.
At shutter speeds longer than 1/200, the rear curtain doesn't start to close until some time after the front curtain has dropped all the way down. At shutter speeds faster than 1/200 the rear curtain starts to close BEFORE the front curtain has fully opened making the shutter opening a slit. The slit gets smaller as shutter speed is increased as the rear curtain has to start closing sooner and sooner after the front curtain starts to move.
The speedlight has to fire multiple times during an FP exposure so the image sensor sees a lit scene for each width of the slit. The faster the shutter speed, the narrower the slit, the more times during a single exposure the speedlight has to fire.
The speedlight cannot fire at full power and still have enough time to recharge the capacitors for another full power shot. Even firing rapidly at only partial power is very draining on the speedlight's batteries.