Just think about any acceleration that is only explicitly dependent on time. The velocity is the first integral, the displacement the second. The real applications (electrical circuits, mass/spring systems, quantum mechanics) are in the field of differential equations, which is basically integration on steroids. The applications of the Fundamental Theorem of Calculus are extraordinarily widespread. I say it like this: "The Fundamental Theorem of the Calculus is responsible for the modern, technological age." So there you go.