I saw no explosion in the video...at the :28 mark. What I saw was a missile going down range. The higher a missile or rocket climbs, there is less atmospheric pressure. That allows the exhaust to expand outward. I figure, to get suborbital, it has to travel 18K to 19K mph. If you saw it for 10 minutes, you probably saw it go over the horizon.
I read a long time ago, the Trident missile (don’t know which model) is exceeding 13,000 mph two minutes after launch. Sub-orbital velocity may indeed be higher, when the platform rotates (PAM) to kick off the warheads.