Does AF works on Nikkor 50mm when I add Extension Tube?

I have Nikon D3000 and I bought lately Nikkor 50mm 1.8D lense for still life shots, since my camera Nikon D3000 has not build in focus motor, could an extension tube with AF engine made the AF work!

No, such an extension tube would merely transmit the torque of an autofocus motor in the camera to the lens, it does not contain an own autofocus motor.

No, nor should it.

Shooting close ups has never been an auto-focus process. The extension tube is attached the lens and then the camera is moved in and out to bring the subject into focus. Actually, the same is true when using a macro lens, even it it is an AF-S lens.

You pick the image to subject ratio you want and then move the camera to focus the subject. This assures that the image to subject ratio is as required.

The AF 50 mm f/1.8 lens must be manually focused with your camera, why would you think an extension tube would change that?

You do know that to use the auto-focus feature of your fine camera, you must buy AF-S Nikkor lenses, right?