In The First Avenger, during the dummy grenade scene, was Agent Carter attempting to jump on the grenade? She runs towards Steve/the grenade? Is there any confirmation that she intended to do the same?
The script (pg 25) indicates that she did intend to dive on the grenade:
COLONEL PHILLIPS (CONT’D) GRENADE!
It tumbles in the grass, stopping in front of the recruits. Steve’s eyes go wide.
The rest of the recruits scramble away. HODGE YELPS. HE THROWS HIMSELF UNDERNEATH A NEARBY JEEP.
PEGGY MAKES FOR THE GRENADE, BUT STEVE GETS THERE FIRST, THROWING HIMSELF ON IT.
Steve was closer and got there first. As for her standing around by Steve while he lays on the grenade, I'm guessing she's just a little smarter and quickly figured out what Colonel Phillips was doing. Especially since in the script (but not the film), the Colonel is standing next to a labelled crate of dummy grenades:
PAN TO THE CRATE, WHICH WE SEE IS CLEARLY LABELED: “M-56 TRAINING GRENADES - INERT.”