As pointed out in Medix2's answers, the rules are not very clear and leave a lot of space for interpretation.
I think that it depends on the size of the backpack, besides the encumbrance.
As a DM, I would consider backpacks with size about the one of the boy-scouts', with all the stuff not needed for the combat (food, rope, etc etc) optimally "compressed" and moreover with a bedroll packed in the top of it. So, trying to be quite realistic, I like to think that for removing such a backpack there are two options:
- using one action
- using the movement (or half of it, if it seems too much)
In the last case, some special cases must be considered (e.g. the Rogue class with its cunning action).
For example, if your PC has a big backpack with a lot of food rations, a couple of weapons, some clothes, the bedroll, the classical 15 foot rope, some tools (e.g. thieves' tools), a torch, oil for torch, a couple of scrolls with maps and a tent I think that it takes some effort to remove such backpack: this effort can be translated in game with using an action or using the movement.
Otherwise, if your PC has a simple sack (without laces) with only clothes I think that it is much easier to remove it.
To be honest, as DM I used this approach once or twice: the Barbarian Dwarf in the party was carring a backpack with an armor, food rations, a couple of weapons (besides two axes that was carrying), 1-2 potions and all his adventuring gear. We decided to apply the (total) Movement equivalence to remove the backpack, and it worked quite well.