Land Speed Record Broken: 0-6,400 in Six Seconds
Stop thinking about averages. It's accelerating the whole time, and the 6400mph number is the maximum speed. If it started that last 1.3s at a fairly low speed and only achieved the max towards the end, you'd still come out with an average speed for that segment in the range you mention.
A car that can go 0-60mph in 10s and use 200 feet of road in the process only averages 13mph in that 200 feet, but it's certainly travelling much faster than that at the end.