Use a clothing iron and a towel, warm the vinyl (through the towel) until it's pliable, lay it down, in place, put a heavy book on the ripped area, then put something heavier (like a concrete block) on top of the book. Let it sit for several hours or better yet, overnight, then use the seam sealer in the above post to "secure the edges of the cut.
Alternatively, find a vinyl floor installation/service center and talk to them about a "professional repair"... Don't be surprised if they arrive with an iron, a towel, a book and a concrete block in one hand and a vinyl repair kit in the other.....
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS