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This photo of some fun 4th of July fireworks was taken at about f/8 at 6" sec. (The shutter was open for 6 full seconds.) I definitely had to use a tripod, and I used a remote to make sure that the camera would not move when I pressed the shutter button.
This photo of my little boy swinging was taken at about 1/800th of a second. He was moving fairly fast, and I wanted to stop the action and avoid him being blurry. Faster shutter speeds freeze action and avoid motion blur.