Let's carefully analyze the motion of each object to determine the distance and displacement. Upon finding these values, we'll identify which object meets the condition where the distance is three times as great as the displacement.
### Object W:
- Motion: 3 units left, then 3 units right
- Distance Traveled:
1. 3 units left: 3 units
2. 3 units right: 3 units
- Total distance = 3 + 3 = 6 units
- Displacement:
1. 3 units left: -3 units
2. 3 units right: +3 units
- Total displacement = -3 + 3 = 0 units
### Object X:
- Motion: 6 units right, then 18 units right
- Distance Traveled:
1. 6 units right: 6 units
2. 18 units right: 18 units
- Total distance = 6 + 18 = 24 units
- Displacement:
1. 6 units right: +6 units
2. 18 units right: +18 units
- Total displacement = 6 + 18 = 24 units
### Object Y:
- Motion: 8 units left, then 24 units right
- Distance Traveled:
1. 8 units left: 8 units
2. 24 units right: 24 units
- Total distance = 8 + 24 = 32 units
- Displacement:
1. 8 units left: -8 units
2. 24 units right: +24 units
- Total displacement = -8 + 24 = 16 units
### Object Z:
- Motion: 16 units right, then 8 units left
- Distance Traveled:
1. 16 units right: 16 units
2. 8 units left: 8 units
- Total distance = 16 + 8 = 24 units
- Displacement:
1. 16 units right: +16 units
2. 8 units left: -8 units
- Total displacement = 16 - 8 = 8 units
### Conclusion:
To find the object for which the distance is three times the displacement, we check the calculations:
[tex]\[
\text{Condition: Distance} = 3 \times \text{Displacement}
\][/tex]
For each object:
- W: 6 ≠ 3 × 0
- X: 24 ≠ (3 × 24)
- Y: 32 ≠ 3 × 16
- Z: 24 = 3 × 8
Thus, the object that has a distance three times as great as its displacement is Object Z. The distance is 24 units and the displacement is 8 units.
