From the provided position-time graph, we can determine both the magnitude of displacement and the total distance traveled by analyzing the movement of the object.

Key points:

• Initial position (at $t = 0$): 0 meters.
• Final position (at $t = 10$ seconds): approximately $-7$ meters.
• Displacement is the change in position from the initial to the final point.

1. Displacement

$\text{Displacement} = \text{Final Position} - \text{Initial Position} = -7 - 0 = -7 \, \text{meters}.$ The magnitude of displacement is 7 meters.

2. Distance Traveled

The distance traveled accounts for the total path taken by the object, not just the net change in position. Here’s how the object moves:

• From $t = 0$ to $t = 2$, the object moves from 0 to 5 meters: distance = 5 meters.
• From $t = 2$ to $t = 5$, the object stays at 5 meters: distance = 0 meters.
• From $t = 5$ to $t = 7$, the object moves from 5 meters to $-4$ meters: distance = 5 + 4 = 9 meters.
• From $t = 7$ to $t = 10$, the object moves from $-4$ meters to $-7$ meters: distance = 3 meters.

Thus, the total distance traveled is: $5 + 9 + 3 = 17 \, \text{meters}.$

Final Answers:

• Magnitude of displacement: $7 \, \text{meters}$.
• Total distance traveled: $17 \, \text{meters}$.

Would you like further clarification or more details on any step?

Here are five related questions:

1. How is displacement different from distance traveled in motion analysis?
2. What would happen if the object returned to its starting position?
3. How can you calculate average velocity using displacement and time?
4. What is the significance of the slope of the graph in a position-time graph?
5. How can you determine instantaneous velocity at any point from this graph?

Tip: Displacement is always the straight-line distance between the start and end points, while distance is the sum of the total path traveled, considering all changes in direction.