It’s a touch ironic, but conveying a sense of movement in a photo is more readily achieved by slowing down the shutter speed. Using a fast shutter speed freezes movement. The results may be pin-sharp but they can look oddly static. However, the longer the shutter speed, the more any movement during exposure is blurred and softened.
Take a look at the two photos above. The top photo was shot with a fast shutter speed: 1/750 of a second. The lower photo with a much slower shutter speed: 1/10 of a second (which required using the smallest possible aperture on the lens and base ISO on the camera – though I could have achieved a similar effect by using an ND filter).
The first photo looks like a sedate day at the fair, the second like a white-knuckle ride of terror. It wasn’t of course, but this is the impression you’d come away with if you didn’t any know better. So, when you want your subject to look as though it’s moving try slowing down rather than speeding up…