Well, it IS a 1km RUN. Mathemagically, it's ~17m/s which is a lot.
I know. I just think that one month isn't enough to go from getting tired by 100m to a full km under 5m. I'll get off my ass tomorrow and begin.
just push through and keep running as long as possible even after you want to fall over and die.
In high school I figured out that if I just blitz ran for as long as I could and walked the rest I'd get a better time than if I tried to pace myself.