Uechi-ryu has many movements that give the practitioner the opportunity to practice explosive movements solo, and with partners. And for a system that focuses on close-in or close combat fighting, being able to learn and use these techniques is an important, though not the only, step to your success.
I suggest reading more about the theory and application of explosiveness, and how it applies to Uechi-ryu. These are two great resources.
- Elements of Fajin in Uechi-ryu Karate, by David Elkins, L.C.S.W.
- Explosive Karate, (1) by Arthur Rabesa (Amazon.com)
- Explosive Karate, (2) by Arthur Rabesa (EasternArts)
Some examples of this explosiveness in action by Wayne Otto, 5 Dan. Though it's kumite, you see the explosiveness and control exhibited.