These colder months mean shorter days with less light and more opportunities to use slower shutter speeds without needing ND filters, so this is a good time to go over this topic…
The faster an object is moving the faster of a shutter speed you can get away with using while still capturing motion blur. Anything 1/30 and slower is a good place to start. Something like 1/10 is ideal – especially if you aren’t using a tripod. Just remember there’s a difference between camera shake and motion blur. At least one thing in the photo must be in sharp focus otherwise the blur in your photo is just undesirable camera shake.
If your lens has some sort of image stabilization and you’re using a wide angle you can get away with using pretty slow shutter speeds and no tripod. The image below I shot handheld with a shutter speed of 1/4.
If a scene is fairly well lit it’s possible to show down the shutter speed just enough to capture motion by closing up the aperture as much as possible. I shot this carnival ride in late afternoon light at a shutter of 1/15 with the aperture stopped down to f/22.
In some cases you can use a flash set with a second curtain shutter to get a trailing effect and a sharp well lit image. What a second curtain shutter does is make the flash go off right before the exposure ends rather than right after the shutter first opens. Doing this makes the trails appear to drag behind the subject in movement rather than through it.
The other way to depict movement in an image is a technique called Panning which involves the camera following the object in movement so the background is blurred rather than the subject. It can be tricky to get the speed in which u swipe the camera to keep up with the moving subject, and the only way to really master it is practice and a lot of trial and error.
I panned the image below at 1/5 on a tripod by just swiveling the tripod to follow the ambulance as it passed by.
This pan I shot handheld with a shutter of 1/40. The shutter was a bit fast so the background blur is very subtle but the subject still pops in comparison.