1. **State the problem:** We need to find the displacement and the total distance traveled by the red ball between 0 seconds and 24 seconds based on its position over time. 2. **Recall definitions:** - Displacement is the change in position from the initial time to the final time, calculated as $\text{displacement} = x_{final} - x_{initial}$. - Distance traveled is the total length of the path covered, summing all movements regardless of direction. 3. **Identify positions at key times:** - At $t=0$ s, position $x_0 = 6$ m - At $t=8$ s, position $x_1 = 15$ m - At $t=12$ s, position $x_2 = 0$ m - At $t=16$ s, position $x_3 = -15$ m - At $t=24$ s, position $x_4 = 6$ m 4. **Calculate displacement:** $$\text{displacement} = x_4 - x_0 = 6 - 6 = 0 \text{ m}$$ 5. **Calculate distance traveled:** Sum the absolute differences between consecutive positions: $$|x_1 - x_0| + |x_2 - x_1| + |x_3 - x_2| + |x_4 - x_3| = |15 - 6| + |0 - 15| + |-15 - 0| + |6 - (-15)|$$ $$= 9 + 15 + 15 + 21 = 60 \text{ m}$$ 6. **Interpretation:** - The ball ends up at the same position it started, so displacement is zero. - However, it traveled back and forth, covering a total distance of 60 meters. **Final answers:** - Displacement = 0 m - Distance traveled = 60 m