Captain Kirk is on an important space mission to bring a Klingon ambassador to space outpost 13. He must travel 6000. 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 870.0 km left to go.
His ship must then accelerate at 20.000 m/s-2 for how many seconds in order to achieve the desired time?
s = u + at
s = vot + 1/2at2
v2 = u2 + 2as
The Attempt at a Solution
I've tried separating the motion of the spacecraft in 3 different times. Time 1 is when the spacecraft is at constant speed until 27.0min, time 2 is when the spacecraft starts to accelerate at 20.000m/s-2 and time 3 is when the spacecraft travels at the new constant speed increased by the acceleration. So:
For time 1:
s = vot
Here i found the speed just by plugging in s = 5130000m and t = 1620s.
For time 2 and 3:
s = vot + 1/2at2 + vf(180-t)
180-t as the spacecraft has 3 minutes remaining (180s). I found the vf with the following equations:
vf = v0 + at
I've tried this problem numerous times and I keep getting that the result is 0.044s, but it is wrong.