Day 45 - Geometric vs. Temporal Movement Search

Just finished watching day 45 and I had a quick question about the geometric movement search (or search in p).

So if you're using a temporal search, you check for an intersection along the movement direction, if there is one move the player there and calculate the remaining velocity after that movement, then repeat until there are no intersections (or bail out).

I was just wondering why you don't have to do this same iteration with the geometric search? Once you've moved the player won't you similarly have some remaining velocity that needs to be resolved?

Am I missing something? :)

Edited by Albert Elwin on Reason: typo!