There are several ways to do this. You could add a blur in post, but that would require a lot of keyframing of masks and might not look realistic. This will depend on the kind of shot you want to pull off, but if you want to replicate the shot from the movie above (in which someone dashes into frame and comes to rest next to another person, who is lying down) it is pretty easy because nothing else in frame is moving and the camera is static.
Assuming you have a camera with manual controls, turn the shutter speed way down. Now when you move the camera, everything goes blurry. You may also notice that your shot becomes overexposed because you are now letting more light into the camera, so you may need to adjust your lighting setup accordingly. Next, put the camera on a tripod. Then, have any actors in the shot remain as still as possible. If they're lying down, that's no problem! Then have your speedy actor rush into frame. They will look all blurry, but they'll be moving at normal speed. Take your video into AE and use time-remapping to make the action happen faster. Now you have a speedy looking actor with a realistic looking blur!
If you want to have other things moving in the scene, you may have to record those using a normal shutter speed and then, with the camera locked off, lower the shutter speed and record your speedy actor. Then, in AE, you can mask out the parts of the video you don't want. There will likely be exposure differences between the two clips, but you could either adjust your lighting on set, work with the exposure effect in AE, or use a combination of low shutter speed and a blur effect in post.