When photographing moving subjects it is all too easy to default to a shutter speed of 1/1000 second or faster to freeze the action. This is a perfectly good portraiture\technique, but very different and more dynamic images can be obtained using much slower speeds.
The two simplest alternatives are to blur the subject while keeping the background sharp, or maintain subject sharpness by panning the camera and letting the background flow. Shutter speeds must be chosen to suit the speed of movement and the desired effect. The camera can be moved horizontally, vertically, diagonally, or even rotated. The direction of movement of the subject, however, has considerable bearing upon the amount of movement relative to the camera and hence the nature of the final image. Movement towards and away from the camera will produce less blurring than movement in the plane of the sensor.
Another technique is to blur everything by using a slow shutter speed and moving the camera relative to both background and subject during exposure. Here the results are more difficult to predict, so try a range of shutter speeds determined by the speed and direction of movement of the subject. It is also possible to create the impression of movement for stationary subjects. Set a camera to a slow ISO speed, perhaps ISO 50, attach a zoom lens and attach it to a stable tripod. Position the subject, perhaps a child on a bicycle, in the centre of the frame. Focus on the child with the lens at maximum focal length and then zoom back to check the framing of the wider picture. Select a slow shutter speed and a small aperture - perhaps 1/15 second at f/8 or f/11. Release the shutter while moving the zoom from maximum to minimum focal length. The result should be a reasonably sharp subject at the centre of the image surrounded by a motion-like blur of converging streaks.