I'm not certain how to solve this, as the acceleration is not constant and dependant on the velocity. Here's the problem:

I take it I need to integrate the acceleration function, but I don't know how when I have dv/dt = -3.10 (dx/dt)^2. As this is just an introductory physics class and we are barely two weeks in, I'm wondering if there's not a simpler way to look at this. Any help pushing me in the right direction would be extremely appreciated!

I haven't learned differential equations yet. Is there no other way to solve it? I tried moving the v and dv to one side and the constant and dt to the other and solving it like that, but that didn't work..