We Video is a free online video editor. To access it for free, there are a couple of limitations. The application will limit videos to 5:00 in length, which generally speaking is more than enough for any class project. If needed, a student could separate their video into parts and submit it in segments for grading.
The free We Video also limits users to 1GB of storage.
Finally, We Video will put a watermark on videos that were created using their free utility, but the brain tunes that out quickly.