Someone is going to ask this, so it may as well be me. You should probably give the context for this problem, since it's not clear what is going on from the information you've quoted. What does "a relative speed of 1200 m/sec" mean? This is relative to what?
I take it that a 25,000 N force is being applied to the mass for 2 seconds. It's not clear how to proceed until we know what that velocity is for...
a 1.0*10^4kg spacecraft is traveling through space with a speed of 1200 m/s realtive to earth. a thruster fires for 2.0 min, exerting a continuous force of 25kN on the space craft in a direction opposite the spacecrafts motion . calculate the initial momentum and the fianl momentum kof the spacecraft.
Thank you! So we will be using velocities relative to the Earth for these momenta. You have already found the initial momentum, p_i (what is it?).
What is the relationship between force and change of momentum? You can find the momentum change caused by the thruster, which will let you find the final momentum. (Your equation has the right ideas, but in the wrong sequence...)
You are correct insofar as the impulse, which is equal to the average force times the time during which it is applied, is equal to the change in momentum, p_f - p_i . So the only thing that needs to be corrected is
Your left-hand side is fine. The right-hand side is the change in momentum. You already have the mass in the first term there, so I have corrected the factor that should be just the final velocity.
Since you are just asked for the initial and final momenta, you really only need to calculate the products. You already have the one for the initial momentum, so you now just need to find the first product on the right-hand side, which is the final momentum.