Adding blurs or motion blur to something animating in After Effects is involved in itself. See Adobe AE Help: Motion Blur (or Ray-Traced 3D — more), Clarifying Blurs, Blurs: Effects A-Z & Beyond, and CMG Hidden Gems: Chapter 8 – Motion Blur and More by Chris and Trish Meyer here on PVC.
You can add motion blur to video or 3D renders with AE's CC Force Motion Blur or Time Warp filters or with ReelSmart Motion Blur. Both of the latter 2 filters use motion estimation for better results, as noted in After Effects Help:
“To achieve a result similar to the result of ReelSmart Motion Blur, apply the Timewarp effect, set Speed to 100, enable motion blur within the effect, and use the manual shutter control features to adjust the motion blur.”
Todd Kopriva notes that After Effects CC (12.0) has a “new Pixel Motion Blur effect …a simpler way of using technology built into the Timewarp effect to 'fake' motion blur.” He also recommends Pixel Motion Blur in After Effects CC by Chris and Trish Meyer here on PVC.
Awhile back, Aharon Rabinowitz posted video tutorials of this in Quick Tip: Adding Motion Blur Into Your Video and CC Force Motion Blur, while Curious Turtle posted Faking Motion Blur. For another demo, Motionworks posted a video tutorial by Grischa Theissen on using ReelSmart Motion Blur on footage created in Cinema 4D. See also More slow motion from pictures using Pixel Motion on AE Portal archive (Pixel Motion in AE Help), and Chris & Trish Meyer's CMG Hidden Gems: Chapter 8 – Motion Blur and More.
In another use, some apply RealSmart Motion Blur, or an alternative, to fix the grainy edges on tough roto or keyed mattes. See AE Help for more info and resources on motion blur, and for blurs in general see Blurs: Effects A-Z & Beyond. Here's Aharon and Joren; check out Joren's blog for speed comparisions:
Also, Jack Binks from The Foundry offered advice on the AE-List if you run into artifacts with AE's Timewarp plug-in,
'It depends on exactly what the clip artifacts look like, but normally what you have to do is separate the foreground motion from the background with a little roto. Essentially a retimer works by calculating a vectorfield for the movement of blocks of pixels within the scene. A 4 chan vectorfield (ie forward and backwards u and v) cannot represent pixels which disappear or reappear between frames (ie occlusion), and so pixels in these regions get pushed along with the vectors from the actual blocks detected.
You can persuade most retimers to split a shot into two vectorfield passes, using roto to specify the region split.
You can do this in timewarp using the matte layer and matte channel drop downs. Essentially pop a white solid in the comp of the same dimensions, roto on that solid, drawing around the foreground object in the other layer for reference (roughly to begin with and only refine where it needs it). Then precomp the solid with attribs. In the Timewarp matte layer drop down pick the precomposed layer, and in the channel pick luminance. You can trouble shoot to check that the correct matte is being fed in by momentarily switching the 'show' to 'matte' and check that the correct matte is fed back out.”
And Chris Meyer added, “FWIW, I've found the Tuning > Vector Detail and Block Size parameter to be the most fruitful to tinker with for problems like these… in general, I have a lot more “issues” with Timewarp than I do with Twixtor.' Chris has also noted that you can check out additional details on Timewarp in The Foundry's original Kronos documentation.
Update: Creative Dojo posted results of his speed test in ReelSmart Motion Blur vs CC Force Motion Blur. Also, a few years ago Danie Bachler proposed Using Brainstorm in After Effects to find optimum timewarp settings.
Also, James Whiffin added a survey, A Focused Look Motion Blur In After Effects: