Related, Sprint missile test (anti-ballistic-missile missile). Extremely fast acceleration, you can see in the test footage which is not sped up.
Mass: 7,700 lbs.; Thrust: 650,000 lbs.
Around 100 G of acceleration, reaching Mach 10 within 5 seconds.
"The first stage was exhausted after only 1.2 seconds, but produced 650,000 pounds-force (2,891 kilonewtons) of thrust. On separation, the spent first stage disintegrated due to aerodynamic forces. The second stage fired within 1 to 2 seconds of launch. Interception at an altitude of 1 to 19 miles (1.5 to 30 km) took at most 15 seconds."
https://en.m.wikipedia.org/wiki/Sprint_(missile)
Nuclear tipped SAM isn't too crazy for the time. They were defending against nuclear-armed supersonic bombers and knocking out multiple with one missile was good idea. Early SAMs also weren't that good.
There were lots of nuclear tactical weapons (some bonkers) at the time. Nuclear torpedos. Nuclear anti-submarine rockets. Nuclear artillery shells. Nuclear tactical rockets.
