Maya: Motion Blur.
Add perceptual blur as objects move quickly, mimic film

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Create an animation:
Animate an object to move quickly across the screen.

Arnold:
This will blur the shadow.
Open Windows->Rendering Editors->Render Settings...  srender_settings
Select Render Using Arnold Renderer
     Under the Arnold Renderer tab:
          Under the arrow Motion Blur
               Select Enable

Render a frame from the middle of the animation.



Maya Software:
This does not blur the shadow.
Open Windows->Rendering Editors->Render Settings...  srender_settings
Select Render Using Maya Software
     Under the Maya Software tab:
          Under the arrow Motion Blur
               Check Motion Blur
                         Select 3D

Render a frame from the middle of the animation.

If you do not see enough blur, increase blur by frame

Try 2D motion blur if you like, it is a little strange



Mental Ray:
This will blur the shadow.
Open Windows->Rendering Editors->Render Settings...  srender_settings
Select Render Using mental ray
     Under the Scene tab:
          Under the arrow shutter
               Select Motion Blur Full

Render a frame from the middle of the animation.

If you do not see enough blur, increase Motion Blur By