In sports photography, and most photography in general, the standard practice is to choose a shutter speed that freezes the action. That’s usually somewhere around 1/1000 of a second in sports. It’s fun to go against that and purposely introduce blur sometimes though, particularly in scenes where either the subject is perfectly still and everything is in motion around them, or the other way around where the subject is moving at a high speed across a still environment. The latter is especially beautiful in the world of motorsports, since the subject itself (the car) keeps its shape even while moving at high speeds, as opposed to the windmilling arms and legs of a human athlete.
The process is pretty simple. Select a slower shutter speed, something like 1/60 of a second or slower, and adjust aperture higher to compensate. The trade-off with depth of field from a narrow aperture is negligible in this case. Then, pan with the subject as you shoot, keeping them as still as possible in the frame. The vast majority of your shots will end up as blurry, non-comprehensible messes. But every now and then when done properly, and with a healthy bit of luck, you’ll get some stunning images of a sharp subject, racing across a blurred landscape. It conveys speed and energy in a way that a still background can’t. It also allows larger showcases of landscape without taking focus away from the subject.
I love using this technique whenever I shoot NASCAR or F1. Some photographers take it to the next level. Darren Heath (@artoff1 on Instagram), for example, is known for his dramatically slow shutter speed, vast-frame shots of F1 car racing across massive, smeared landscapes. It’s out of the box, dramatic, and oh so beautiful.