Forgive me. When I hear a person say "I'm not quite sure",
what I hear is "I have no clue".
This is not an awfully tough problem, but there IS one big piece of information missing: When the 'burners' ignite, do they push in the same direction it's already moving, and speed it up ? Or do they push opposite to its motion, and slow it down ?
the question doesn't say.
For reasons that I won't go into, I think we should assume that the 'burners' are
on the back of the rocket, pushing in the same direction it's already going, and
speeding it up.
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So we have a 1,000 kg object. Suddenly a force of 200N kicks it from behind,
and starts speeding it up.
Do you remember . . . (Force) = (mass) x (acceleration) ?
We know the force and the mass . . . (200N) = (1,000 kg) x (acceleration)
Acceleration = 200/1,000 = (0.2 meter per second) per second.
That's how its speed grows during the burn.
In 300 seconds, it will gain (300) times (0.2 meter per second) = 60 m/sec.
It was originally moving at 40 m/s and the 'burners' added 60 m/s during
the 5-minute burn. So when the burners shut off, it's moving 100 m/s.
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If the burners were pushing the other way, slowing it down, then in 300 sec
it would lose 60 m/s of speed. Its final speed would be (40) + (-60) = -20 m/s.
That means 20 m/s in the opposite direction.
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That's the answer you need, and the math you use to find it.
But there's still something wrong with this problem ... in the real world
of space travel, it's a bogus question. The ship doesn't remain 1,000 kg
while the thrusters fire for 5 minutes. The thrusters use fuel to burn, and
the mass of the ship keeps decreasing and decreasing while fuel burns.
So when the real aerospace engineers do this same problem, they still
use (force) = (mass) x (acceleration), but they're working with a mass that's
constantly changing. You can see that this makes the problem a little more
complicated, and to work it, they use "Calculus". You can get into Calculus
before you graduate High School, if you want to. The things you can do with it
can really give you a feeling of power.
