Auto focusing trouble with my nikkor 50mm 1.8d?

I bought this 50mm lens at a garage sale today for my Nikon D90, I got it for 40$ so I can't complain about the price that's for sure; but upon trying it out at home I soon realized that it can't auto focus which is strange since the D90 is supposed to have a built in auto focus motor I thought, although I do not have any other manual-only lenses so I'm not sure if it's a lens problem or a camera problem. When I manual focus with the lens it does feel a little bit dirty or sandy, as if some little bits of sand or something may be stuck inside the focus ring; would that possibly stop it from auto focusing? Is there something I'm doing wrong? Like some obvious setting I need to activate to turn on the auto focus motor? Also (this is a really dumb question) is it possible the grains of sand might fall back into the camera damaging or dirtying the sensor or something? In which case should I not be using the lens at all… I know I'm asking a lot of questions here, but I would appreciate an answer so much!

Added (1). Fhotoace - Can you at least say why it is such a "dreadfully wrong" problem with the lens? Because from the shots i've taken so far I would say it works perfectly fine (apart from the AF not working, which is what I'd really like to get an answer about).

That is a $135 lens when new.

When a lens feels gritty when manually focusing it, there's something dreadfully wrong. It may coast more to have it cleaned and repaired than it costs to buy a new one.

If your fine D90 can auto-focus with your other lenses, you can't blame your camera for a problem which is probably a problem with the lens