You are tracking the velocity and position of a rocket-propelled object near the surface of mars. The velocity is v(t) and the position is s(t), where t is measured in seconds, s in meters, and v in meters per second. It is known that the v(t)=ds/dt=4.94-3.72t and s(0)=5. A, A. Explain why the condition "f is continuous over [a, b]" from the Evaluation Theorem is fulfilled by this scenario. B. Explain why the condition "F is any antiderivative of f on [a, b]" from the Evaluation Theorem is fulfilled by this scenario. C. Determine the position function s(t) using the initial condition that s(0) = 5. D. Apply the Evaluation Theorem to this scenario to compute between 1 and 3 v(t)dt. Focus on D. In words describe what s(1) means. s(3) in words explain what this means. s(3)-s(1) explain what this means. Is the definite integral in part D equal to s(3)-s(1)? If yes, then this is an application of the evaluation theorem.