Question

Captain Kirk is on an important space mission to bring a Klingon ambassador to space outpost 13. He must travel 1000. 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 199.0 km left to go.
His ship must then accelerate at 8.15 m/s2 for how many seconds in order to achieve the desired time?

Answer 1

The distance he had already traveled is:
7000 m - 1204 m = 5796 m.

Because he went this distance in 27 minutes, he was traveling at
( 5796 m / 27 min ) x (1 min / 60 s) = 3.577778 m/s.

The equation for position is:
s(t) = s0 + v0t + .5at2, where s0 is the initial position (we'll call this 0), v0 is the starting speed (the 3.577778 m/s he was already traveling at) and a is the acceleration (41.14m/s2). Because the position he needs to reach is 1204 m away, we can find the time by plugging everything in and solving for t.

1204 = 0 + 3.577778t + .5(41.14)t2

Arranging everything into a quadratic equation:

20.57t2 + 3.577778t - 1204 = 0

Using the quadratic formula:

t = {-3.577778±√[3.5777782 - 4(20.57)(-1204)]}/[2(-1204)]
t = 7.56 s or -7.73s
Because I'm guessing Kirk hasn't fitted the Enterprise with Doc Brown's flux capacitor yet, the time needed would have to be positive, so he needs 7.56 seconds to reach the destination.



Because he only had 30 minutes, and wasted 27 minutes of it, the 7.56 needed to reach the destination would make him too late.

Answer 2

Most problems like this can be solved using quadratics, just for future reference.

Answer 3

thanks a lot! Though I have already gotten the correct answer!

Answer 4

@iamdoris How you did you approach the question?