Seems like the higher end models have more of a true autofocus that will work with any lens but models like the D3000 will only auto focus with certainl lenses.
The higher end models don't have "true" autofocus. They just support the older way of autofocusing as well as the newer way. The older way was a focusing motor built into the camera with a long screwdriver that fed into the lens to move the elements in the focusing process. It was slow and noisy compared to modern methos.
Later, Nikon put micro motors into their lenses and these don't require the motor in the body with the screwdriver. These are called AFI lenses and autofocus and the entry level Nikons. You won't find this on any new Nikon lenses. Tamron still uses this method.
All new Nikon designs are called AFS and mostly use SWM motors. That is short for Silent Wave Motor. These are sonic ring motors build into the lens. They are usually silent, fast and accurate. Sigma also called this technology HSM for Hypersonic Motor.
Every focal length there is is covered by SWM or HSM or BIM or whatever lenses with motors in them and will autofocus on a D3000 or D5000. There are a few fixed focal length lenses like the 85 f/1.4 that won't. For example, Nikon makes a 60 f/2.8 Macro AF-D macro lens that won't AF on those cameras, but they also make a newer 60 f/2.8 AFS that does and it's a better lens in all ways.
One nice thing is that the entry level Nikons will allow you to mount and will work in manual mode nearly every lens ever made to fit a Nikon since 1959 without alteration or an adaptor. You might have to manually focus or maually set exposure, but they work just fine. So, you can have fun at garage sales, knowing that if you find some $10 Nikon lens, it will work.
For exposure on those anchient lenses, but guess, look at the picture on the back and adjust. It's easy and fun. You can find some excellent and legendary glass that way. People with the higher end Nikons often have to have the lens altered by grinding auto indexing notches in the mount, but not the entry level models.
Just to show you, I'll list all the lenses that autofocus on a D3000 and D5000
Nikkor:
AF-S DX 10-24mm f/3,5-4,5 ED G New
AF-S DX 12-24mm f/4.0G ED-IF
AF-S 14-24 mm f/2,8G ED
AF-S DX 16-85mm f/3,5 - 5,6G ED VR
AF-S 17-35mm f/2.8D ED-IF
AF-S DX 17-55mm f/2.8G ED-IF
AF-S DX 18-55mm f/3.5-5.6G
AF-S VR DX 18-55mm f/3.5-5.6G
AF-S DX 18-70mm f/3.5-4.5G ED-IF
AF-S VR DX 18-105 f/3.5-5.6G ED
AF-S DX 18-135mm f/3.5-5.6 ED-IF
AF-S VR DX 18-200mm f/3.5-5.6G IF-ED
AF-S 24-70 mm f/2,8G ED
AF-S 24-85mm f/3.5-4.5G IF-ED
AF-S VR 24-120mm f/3.5-5.6G ED-IF
AF-S 28-70mm f/2.8D IF-ED
AF-S 35mm f/1.8G New
AF-S 50 mm f/1,4G
AF-S DX 55-200mm f/4-5.6G ED
AF-S VR 55–200mm f/4–5.6G IF-ED
AF-S 60mm f/2.8G Micro
AF-S VR 70-200mm f/2.8G ED-IF
AF-S VR 70-300mm f/4.5-5.6G
AF-S 80-200mm f/2.8D ED-IF
AF-S VR 105mm f/2.8G Micro
AF-S VR 200mm f/2.0G ED-IF
AF-S VR 200-400mm f/4.0G ED-IF
AF-I 300mm f/2.8D IF-ED
AF-S 300mm f/2.8D IF-ED
AF-S 300mm f/4.0D ED-IF
AF-S VR 300mm f/2.8 ED-IF
AF-I 400mm f/2.8D IF-ED
AF-S 400mm f/2.8D ED-IF
AF-S VR 400mm f/2,8G ED
AF-I 500mm f/4.0D IF-ED
AF-S 500mm f/4.0D ED-IF
AF-S VR 500mm f/4G ED
AF-I 600mm f/4.0D IF-ED
AF-S 600mm f/4.0D ED-IF
AF-S VR 600mm f/4G ED
Sigma:
4,5mm f/2,8 EX DC HSM
10mm f/2,8 EX DC HSM
10-20mm f/4-5.6 EX DC HSM
10-20mm f3,5 EX DC HSM New
12-24mm f/4.5-5.6 EX DG HSM
14mm f/2.8 EX
17-35mm f/2.8-4.0 EX DG
17-70mm f/2.8-4.5 DC Macro HSM
18-50mm f/3.5-5.6 DC HSM
18-50mm f2,8-4,5 DC OS HSM New
18-50mm f/2.8 EX DC Macro HSM
18-125mm f/3.8-5.6 DC OS HSM
18-200mm f/3.5-6.3 DC OS
18-250mm f3.5-6.3 DC OS HSM New
24-70mm f2,8 EX DG HSM
30mm f/1.4 EX DC HSM
50mm f/1.4 EX DG HSM
50-150mm f/2.8 EX DC HSM
50-200mm f4-5,6 DC OS HSM New
50-500mm f/4.0-6.3 EX DG
55-200mm f/4-5.6 DC HSM
70-200mm f/2.8 EX DG Macro
70-300mm f/4,0-5,6 DG Macro
70-300mm f/4,0-5,6 DG APO Macro
80-200mm f/2.8 EX DG Macro
80-400mm f/4-5.6 EX OS
100-300mm f/4.0 EX DG
120-300mm f/2.8 EX DG
120-400mm f/4.5-5.6 DG OS APO HSM
150mm f/2.8 EX DG Macro
150-500mm f5-6.3 DG OS APO HSM
180mm f/3.5 EX DG Macro
300mm f/2.8 EX DG APO HSM
300-800mm f/5.6 EX DG APO
500mm f/4.5 EX DG HSM APO
800mm f/5.6 EX DG APO
Tamron:
10-24mm f/3.5-4.5 Di II LD New
17-50mm f/2.8 XR Di II
18-250mm f/3.5-6.3 Di II
18-270mm f/3,5 -6,3 Di II VC LD
28-75mm f/2.8 XR Di LD
28-300mm f/3.5-6.3 XR Di VC
70-200mm f/2.8 Di LD MACRO
70-300mm f/4-5.6 Di LD Macro
90mm f/2.8 Di Macro II
Tokina:
12-24 f/4 AT-X 124 PRO DX II New
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Cheers, Craig