Final answer:
Without the actual step response function of the LTI system, we cannot determine the impulse response. The step response's derivative is what gives us the impulse response of the system.
Step-by-step explanation:
The student is asking for assistance in finding the impulse response (h(t)) of a causal linear time-invariant (LTI) system when given the system's response to a step input, x(t)=u(t). To find the impulse response of the system, one typically would use the derivative of the step response, as the impulse function is the derivative of the step function in the context of LTI systems. This procedure is based on the relationship between the system's output to a step input (step response) versus its output to a Dirac delta function (impulse response).
However, the provided excerpts from the context do not directly relate to the question at hand, since they discuss topics like simple harmonic motion, motion equations, and force impulses in physics. This appears to be information unrelated to the student's query regarding the response of a causal LTI system in electrical engineering or signal processing contexts.
Without the specific step response of the LTI system, we cannot accurately determine the impulse response through calculation in this instance. To proceed, the actual function or graph characterizing the step response should be provided. Once we have that information, we can find the derivative of the step response to obtain the impulse response.