According to http://ffmpeg.org/ffmpeg-filters.html#crop the expression 
variables for t (time in seconds) and n (frame number) are available.

# X distance per frame = (400 - 0) / (10 * 25) = 1.6
# Y distance per frame = (10 - 0) / (10 * 25) = 0.04

I suspect you'll want something similar to the following.

-vf "crop=enable=lt(t\,10):w=1200:h=980, 
crop=enable=between(t\,10\,20):w=1200:h=980:x='(t-10)*1.6':y='(t-10)*.04', 
crop=enable=gte(t\,20):w=1200:h=980:x=400:y=10"

-----Original Message-----
From: ffmpeg-user [mailto:ffmpeg-user-boun...@ffmpeg.org] On Behalf Of Paul B 
Mahol
Sent: Wednesday, 27 January 2016 05:35
To: FFmpeg user questions
Subject: Re: [FFmpeg-user] How to pan hozitonally on a video?

On 1/26/16, Sub Phil <phil40...@gmail.com> wrote:
> RE:https://www.ffmpeg.org/ffmpeg-filters.html#zoompan
>
> Hi,
>
> I have a 30 sec video in 1920x1080@25fps
>
> I want to pan/crop with a constant rectangle of 1200x980
>
> It rectangle starts at position (0,0) till t=10 sec than from t=10 sec 
> to t=20sec I wish my rectangle to move at a constant/linear speed from 
> position (0,0) to (400,10)
>
> Than from t=20 sec onwards, rectangle stays at (400,10).
>
> How can I do that??

Using crop filter and some kind of expressions for x and y.
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