Final answer:
The question cannot be definitively answered with the provided information as it lacks the context necessary to discern which h(t) equation is correct, though it is clear that x(t) and h(t) are related to signals and systems engineering concepts.
Step-by-step explanation:
The question at hand is related to the subject of signals and systems within electrical engineering, and it is concerned with determining the correct formulation of x(t) and h(t). The equation x(t) = u(t-3) - u(t-5) represents a signal x(t) that is turned on and off at different times, with u(t) denoting the unit step function. Based on the provided information, we cannot definitely identify an equation for h(t), but looking at the answers provided, we can conclude that h(t) is expected to involve an exponential term that is modified by a unit step function to ensure causality. Moreover, equations involving displacement, velocity, and acceleration in simple harmonic motion (SHM) were referenced, though they may not relate directly to the question as the signal definitions here do not inherently align with SHM.
Overall, without additional specifications, such as the system's response or initial and boundary conditions for the given signals, it is not possible to determine a unique correct answer from the options provided. It's crucial to understand the context, such as whether the system is causal or if additional conditions like specified values of the signals at moment t are given, to properly decide which option is accurate.