I go to my backpack and I see I have lots of speed-ups just sitting there. However, they are useless..

I assume you are clicking on the right menu to view your inventory. You can't use speedups from there. It's just showing your inventory available. Some items have a "use" button because they need to be opened, such as chests or pouches. Others can be exchanged and also have a "use" button.

The speedups in your backpack don't have a "use" button because they are already unpacked and they are used for a specific task. A task has to be started before you will have the option to use the speedups from the speed up menu of the building, research, training etc.

In other words, those are not extra stored speedups. They are the same ones you will see when you click speed up on a task.

Speedups are used when training troops, upgrading buildings or doing research. When you are doing one of these activities you will have an option to speed it up. For example in the research option after you start a research you have the option to request help and then to speed up.

Tap this and you will get a list of the applicable speedups you own and the option to use them.