Since TV animation tends to have smaller budgets than feature animation, we are often times limited in the kind of animation we can do in terms of backgrounds.  Here are a couple workarounds I have to show movement in a background.  

The first is a tracking shot into cam where our Character is running without gaining away or from cam (but they could if you wanted) The foreground is the ground plane which is just a simple looping set of lines. The BG is actually a static image that would slowly drift down towards the horizon line imitating movement away from the background. 

The second is also a tracking shot where the character is more in profile. This one requires some soft focus and low detail background drawings (usually not a lot, maybe 3 looping images. I only used 2 here but the theory holds.

The last one only requires a single background layout, but we use the camera to imitate action as it pulls out over a static image.