Do you know your kinematic equations? Typically I try to actually reason out Physics problems (really understand why something is negative or positive or increasing etc) as this truly helps you to learn the material. However, if you are stuck on a question which actually counts toward your grade then the best way that I've found was to write all known data (not all that data will be explicitly stated, half of classical mechanics is being able to get that one key piece of information based on the data given to you) then write out all equations, plug everything in, see what you can solve for, rearrange equations etc. Basically just solve for everything mathematically and sooner or later you will get the variable they are looking for.
So just to give you a place to start. It sounds like a 1D motion problem (I'm picturing the airplane already on the carrier when it hits the stopping mechanism), so its going to be pretty basic.
What information do you know from the problem?
t(time) = 1.5s as an example.
What other info can you glean from the problem statement? Don't forget about setting up your reference frame so your signs will work out properly (this is a deceleration problem so some things will be negative and others will be zero).
This problem can be done with these two equations:
Vf=Vi + at
Xf=Xi + Vi*t + 1/2at^2
Once again look at the problem, see what data you have (both explicitly stated and implied under the circumstances), make sure your reference frame is set up properly to 1-make some of the math easier and 2-to make sure your signs are consisten. And go ahead and post up your attempt.