Yes, it features an internal silent-drive motor, ensuring autofocus works on all Nikon DX DSLRs, including the D3000 and D5000 series.
While it features a water-repellent coating on the front element, it is not fully weather-sealed. Avoid heavy rain or extreme dust exposure.
It is designed for DX sensors. On FX cameras, it will automatically trigger 'Crop Mode' or show significant vignetting unless used at 16mm.