How can motivation increase productivity?
Generally speaking, motivation is usually temporary and shouldn't be relied on long-term.
That said, motivation can be fantastic for getting started on a task.
One simple hack is to watch an inspiring or motivational video, listen to a podcast, or read something motivational, first thing in the morning or right before you plan to do your work.
I can't exactly explain it, but something about watching/listening to other inspiring stories gets us fired up and ready to take on the world.
As you may or may not know, productivity is about overcoming procrastination and the resistance of getting started.
Using the motivational surge you get after watching one of these videos, etc. can help you overcome this resistance and start making progress towards your goals.
It's like taking a quick motivational shot before diving into any actual work.