1. The problem asks us to determine whether the object is moving forward, backward, or neither at specific points on a position vs. time graph. 2. The key concept is that the direction of motion is indicated by the slope of the position-time graph at each point: - If the slope (derivative) is positive, the object is moving forward (position increasing). - If the slope is negative, the object is moving backward (position decreasing). - If the slope is zero, the object is momentarily stationary (neither moving forward nor backward). 3. We analyze the slope around each given point: - At (1, 2): The graph is rising before and after, so slope > 0, object moving forward. - At (5, -1): The graph is falling before and after, so slope < 0, object moving backward. - At (7, 2): The graph is rising before and after, so slope > 0, object moving forward. - At (8.5, -4.5): The graph is falling before and after, so slope < 0, object moving backward. 4. Summary: - (1, 2): Forward - (5, -1): Backward - (7, 2): Forward - (8.5, -4.5): Backward This interpretation uses the fundamental rule that the sign of the slope of the position-time graph indicates the direction of motion.