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High accelerations

High accelerations

Q: If we use reasonably high constant accelerations, how long does it take to travel across the country, say, or across the planet?
[24 Jan 2002]

A: If we accelerate and decelerate uniformly with acceleration ±a over a total distance s then
time = t = sqrt(4s / a), midpoint speed = v = sqrt(as)
so for a few sample accelerations we have

sa tv
100km 1g202s3.4min 990m/s2210mph
4g101s1.7min 1980m/s4431mph
10g64s1.1min 3130m/s7000mph
1000km 1g639s10.7min 3130m/s7000mph
4g319s5.3min 6260m/s14000mph
10g202s3.4min 9900m/s22100mph
Earth's diameter 1g2340s39min 11459m/s25600mph
4g1170s19.5min 22900m/s51300mph
10g739s12.3min 36300m/s81100mph

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