1. The problem statement, all variables and given/known data The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared, and is given (in SI units) by a = -3.00v^2 for v > 0. If the marble enters this fluid with a speed of 1.50 m/s, how long will it take before the marble's speed is reduced to half of its initial value? 2. The attempt at a solution I know that this question appeared here a while ago (found an archive to this exact one from two years ago) but I wasn't too sure with some of the help they gave so I'm asking again if someone would kindly help. I know that it involves a=dv/dt so that I end up with something like (v2-v1)=-3v^2(t-0). That may be wrong, I'm in a high school AP class and am just starting with some basic derivations in my calc class, so it is very possible that there's a flaw in all that (and in some of my terminology or whatnot) but if I'm on the right track my main concern would be the v^2. I saw on another post that someone did dv/v^2 = -kdt -1/v = -kt +C but I'm not sure how they got there (besides it looking like they took the integral) Again, things may be wrong and I wouldn't be surprised, but any help would be appreciated, thanks.