I am struggling on finding the time it takes the loop of wire to completely leave the field in part a.

I have found the differential equation of motion to me dv/dt+at=g where a is a constant determined to be a=826.72. I found the solution of the DE to be v(t)=g/a(1-e^(-at))

I have tried integrating both the DE and the solution to get position as a function of time, but when integrating, my expressions all have involved the length of the side of wire, l. My professor assures me I do not need that information but I cannot figure out otherwise.

Am I missing something?

LINK TO PROBLEM:

https://imgur.com/a/0T9sF