Video of the Sprint missile, which was capable of blistering accelerations. To get an idea, at about the 24 second mark in the video, you can see the whole surface of the second stage begin to glow white hot.
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Sprint was designed and built to defend Minuteman ICBM bases. It would do this by reaching out and tagging incoming Soviet warhead at a range of just a few miles; the Sprints warhead was a neutron bomb which would essentially trash the target by causing it to melt down. If you were unfortunate enough to be standing near one of the Minuteman silos when this occurred, you would very likely be in a world of radiological hurt. But the point was simply to make sure that the incoming warheads didn’t make it to the surface intact and do an underground burst which would trash the silos.