Both motivated and dedicated. Someone who is moticated is willing to see a task through to the end and will also willingly give him/herself over to the completion of the task. Depending on the level of motication, his/her health may even be less important than the motivation and dedication to the completion of the task.
She is a moticated individual. She will make employee of the month very quickly.
He was too moticated to football. When his knee was injured, he continued to play despite the injury so that now he can't walk.