Depending on the distance of how far your subject is from the camera going in motion parallel to you, does the shutter speed vary or can it be kept the same?

For example, if I was taking a picture of a car 25ft away going 50mph and I had my shutter speed at 1/1000, would I have to change the shutter speed if the car was 50 or 100ft away? Or can I always keep it at 1/1000?

Any help and advice would be helpful and any tips as well, thanks

if the object is further away you may decrease your shutterspeed.

Thanks, I'm getting Annoyed and I'm trying take a picture with depth of field and I'm using a small aperture, in low light but I want the whole scene sharp and on my camera it it shows my subject in focus and the background out of focus, it seems as if no matter what I do zoom in/out move closer or farther nothing works.. I'm using a zoom lens btw 28-105mm

You'll probably need a larger aperture to get everything in focus. I am talking about the F#, not the size of the actual aperture opening.
Ideally, F/22 would do the trick...I can probably guess that your shutter speed would be far too slow at that point.

I thought that the smaller the aperture the slower the shutter speed vice-versa o_o

Again, are you referring to a "smaller" aperture as far as F/#'s go or as far as the aperture hole size?
Large F/# like F/22 would require a slow shutter speed.

So if you take a picture with a 'small' aperture like F/1.8 - you will get a very small depth of field and only a little bit of your subject will be in focus. However, this would allow more light into the camera and let you use a FASTER shutter speed.
http://forums.d2jsp.org/index.php?showtopic=35544551&f=265 is my poorly written guide on this.