Final answer:
The student's question about the distance traveled by the elevator between 8 seconds and 20 seconds cannot be answered accurately due to non-sequential and negative time values provided. For other related questions, principles of kinematics and dynamics, such as Newton's second law and equations of motion, would be used to solve them.
Step-by-step explanation:
The student has asked about the vertical position of an elevator over time and is required to find the distance the elevator travels between 8 seconds and 20 seconds. There seems to be an error in the provided data since the time intervals are negative and non-sequential, which is not practical for plotting a position vs. time graph for an elevator's movement. To accurately determine the distance traveled by the elevator, one would expect a clear, ascending sequence of time values that correspond to the given positions.
However, if we relate to a different part of the question involving a velocity vs. time graph and calculations associated with it (like the instantaneous velocity at certain times, or the tension in the cable), we would use principles of kinematics and dynamics to answer those problems. For example, calculating the tension in the cable when an elevator accelerates or moves at a constant velocity requires understanding of Newton's second law and the equations of motion for linear dynamics.