In the process of point P moving from point A to point D, S increases with the increase of t;

In the process of moving point P from point D to point C, the value of S remains unchanged;

When point P moves from point C to point B, S decreases with the increase of t 。

And because AD=BC, the time from point A to point D is the same as that from point C to point B.

△ the area of △ABP is s max = 12×AD×DC= 10.

The time from A to D to C to B is: 4+5+4)÷ 1= 13 seconds.

So choose a.