Answer:approximately 4.67 m/s.
Explanation:To find the magnitude of the average speed of the particle between t = 1.0 s and t = 4.0 s, we need to calculate the total distance traveled by the particle during this time interval and divide it by the elapsed time.
From the graph, we can see that the particle starts at x = 0 m and moves to the right until it reaches x = 8 m at t = 2.0 s. Then, it moves back to the left until it reaches x = 2 m at t = 4.0 s.
The total distance traveled by the particle during this time interval is the sum of the distances it traveled while moving to the right and while moving to the left. The distance traveled while moving to the right is 8 m, and the distance traveled while moving to the left is 6 m (from x = 8 m to x = 2 m). Therefore, the total distance traveled is 8 m + 6 m = 14 m.
The elapsed time is 4.0 s - 1.0 s = 3.0 s.
So, the magnitude of the average speed of the particle between t = 1.0 s and t = 4.0 s is:
average speed = total distance traveled / elapsed time
average speed = 14 m / 3.0 s
average speed ≈ 4.67 m/s
Therefore, the magnitude of the average speed of the particle between t = 1.0 s and t = 4.0 s is approximately 4.67 m/s.