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Suppose a rocket ship in deep space moves with constant acceleration equal to 9.8m/s^2., which gives the illusion of normal gravity duing flight.

a)If it starts from rest, how long will it take to acquire a speed one-tenth that of light, which travels at 3.0x 10^8 m/s?

b) How far will it travel in so doing?

I will be happy to critique your work.

I couldn't figure out which equation I should use.

You should see that
s(t)=(1/2)a*t^2 and v(t)=a*t
a is 9.8m/s^2
Find the time t needed to = .1c with the second equation and use that for t in the first one. Please post work

v(t) = at
.1c= 9.8m/s^2*t

when I used this t for the first equation I got .000509 butt my book siad the answer was 3.1 x 10^&6 s = 1.2 months

No, c=3.0x 10^8 m/s so .1c=3.0x 10^7 m/s. Thus
3.0x 10^7 m/s=9.8m/s^2*t and t=3.0x 10^7 m/s/9.8m/s^2
You should not get t=.0102s

I got t=3061224.49 and when I pluged t into the second equation I got 4.5918 as the answer

The time looks correct. Keep in mind we only had 2 significant figures to begin with. The distance looks ok too, but I think you're missing an exponent of 10.
It should look like 4.6x10^?
What's the ?(something) here?

would it be 4.6x10^6 ?

Now quit guessing. :)
We know s=(1/2)at^2, v=a*t, a=9.8, c=3x10^8
.1c=3x10^7=9.8*t tells us t is approx. 3x10^6
Thus s=approx. 5x(3x10^6)^2=5*9x10^12=45x10^12 or 4.5x10^13
So it can't possibly be 10^6

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