Question

Captain Kirk is on an important space mission to bring a Klingon ambassador to space outpost 13. He must travel 2000. km in less than 30.0 min, or else war will be declared between the Klingons and humans. After traveling exactly 27.0 min at a steady pace, he sees that there are still 218.0 km left to go.
His ship must then accelerate at 1.49 m/s2 for how many seconds in order to achieve the desired time?

Answer 1

hey! Are you from PHYS 131?

Answer 2

To do this question, you will have to use exactly 30min for the whole trip. So consider letting the ship to accelerate for x seconds, and travel at a constant speed for the remaining time. I got confused by the wording, but that is what you should do. Good luck!

Answer 3

He travels (2000.0 - 218.0 = 1782.0)km in 27 minutes (1620 seconds). You can work out the velocity from this using:
\[v=\frac{s}{t}\]
Then, I think you need to use
\[s=vt+\frac{1}{2}at^2\]

Answer 4

speed with which he has travelled till 27 minutes is equal to

v=1782/27*60= 1100 m/s

distance to be covered = 218000m

s=ut + 1/2 at*t

218000=198000+16200a

20000=16200a

a=20000/16200

=1.2345678

Answer 5

I got confused towards the end, since you're given the acceleration. I guess you have to break it into an acceleration phase, and a constant velocity phase in order to make up the 3 minutes. The acceleration phase would be given by
\(s_1=ut_1+\frac{1}{2}at_1\text{}^2\)
And the constant velocity phase would be given by
\(s_2=vt_2\)

If you say that \(s_2 = 218.0 - s_1\), and that \(t_2 = 180-t_1\), I suppose you'd end up with simultaneous equations that you could solve to obtain t. That seems highly convoluted though!