High accelerations: spoiler
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 = √(4s / a),
midpoint speed = v = √(as)
so for a few sample accelerations we have
| s | a | t | v | ||
|---|---|---|---|---|---|
| 100km | 1g | 202s | 3.4min | 990m/s | 2210mph |
| 4g | 101s | 1.7min | 1980m/s | 4431mph | |
| 10g | 64s | 1.1min | 3130m/s | 7000mph | |
| 1000km | 1g | 639s | 10.7min | 3130m/s | 7000mph |
| 4g | 319s | 5.3min | 6260m/s | 14000mph | |
| 10g | 202s | 3.4min | 9900m/s | 22100mph | |
| Earth's diameter | 1g | 2340s | 39min | 11459m/s | 25600mph |
| 4g | 1170s | 19.5min | 22900m/s | 51300mph | |
| 10g | 739s | 12.3min | 36300m/s | 81100mph | |