A rocketship in free space moves with constant acceleration equal to 32 ft/secondspquared.?

Question

If it starts from rest, how long will it take to acquire a speed one-tenth that of light? How far will it travel in so doing?

Answer 1

Speed of light is about 186000 miles per second so
186000 * 5280 ft/mi = 9.82 E+08 ft/sec
one-tenth the speed of light is 1/10 * 9.82 E+08 = 9.82E+07 ft/s
Divide the desired velocity by the acceleration to get the time:
9.28E+07/32 = 2.9E+06 seconds or 805.56 hours
Now distance is equal to 1/2at^2 which is
x = 1/2*(32*(2.9E+06)^2)
x= 1.3456E+14 ft

Answer 2

c = 3*10^8 so final v is 3*10^7 = c/10
.3048 m = 1ft so
a = .3048*32 = 9.754 m/s²
v = a*t so
t = 3*10^7/9.754 = 3,075,661 s (a bit over 35 days and 14 hours.) and it would have traveled
s = at²/2 = 9.754*3,075,661²/2 = 15,000,000 m

Doug