Ways to create the illusion of movement for still photographs

Hello. What are some creative ways to create the illusion of movement, especially fast movement, for still photographs in an After Effects video?

I'm certainly [not] looking for anything ultra-realistic here, but just the artistic, creative effort of adding a bit of dynamism to a still photo, and give it that illusion of movement. An example that comes to mind is the dashing background behind soccer players in some Japanese soccer anime, but of course I'd love to hear about another creative idea. And examples of photos that I may use with such an effect include a photo of a cropped sports car, and a photo of a cropped athlete just about to shoot a ball or make impact.

Many thanks for anyone taking the time to share tips.

Thank you, Andrey. Andrew Kramer's 3D Compositing video tutorial will surely help.

Hope some others will have extra creative tips to share, especially regarding effects on the still photo itself, or a sort of dynamic background that would make it look like it is moving or dashing.