My camera's shutter speed is really slow even in sport mode

I also need help with my shutter speed in general because it always moves and doesn't stay at one speed. I have a nikon D60.

Learn to use your DSLR on manual mode like it's supposed to be used. That way you tell the camera what to do instead of the other way around.

Hate to say this but time to pull out the instruction book and start at the front and work your way to the back. It took me 3 months working 4 days a week an hour a day to fully understand my Nikon. It should take you less time but not much.

Your shutter speed will not stay at one speed if you are using AUTO modes. It will pick a shutter speed based on the apeture and ASA/ISO setting. If you shutter speed is too slow to capture moving opjects you must do atleast one of the following things. Are a combination of them. Increase your ISO to a higher #. Open you aperuters settinh to a smaller f#. Increase the amount of light on you subject.

Read the manual
Take the camera of Auto everything
Buy a book on basic photography