To determine which of the objects has a distance that is three times as great as its displacement, we need to calculate both the distance traveled and the displacement for each object.
Object W:
1. Moves 3 units left and then 3 units right.
- Distance: [tex]\(3 + 3 = 6\)[/tex] units
- Displacement: [tex]\(-3 + 3 = 0\)[/tex] units
Object X:
1. Moves 6 units right and then 18 units right.
- Distance: [tex]\(6 + 18 = 24\)[/tex] units
- Displacement: [tex]\(6 + 18 = 24\)[/tex] units
Object Y:
1. Moves 8 units left and then 24 units right.
- Distance: [tex]\(8 + 24 = 32\)[/tex] units (distance always positive)
- Displacement: [tex]\(-8 + 24 = 16\)[/tex] units
Object Z:
1. Moves 16 units right and then 8 units left.
- Distance: [tex]\(16 + 8 = 24\)[/tex] units (distance always positive)
- Displacement: [tex]\(16 - 8 = 8\)[/tex] units
Now, we need to check which object has a distance that is three times its displacement:
- For Object W: Displacement is 0, so this cannot be checked because any number multiplied by 0 is still 0.
- For Object X: [tex]\(24 \neq 3 \times 24\)[/tex]
- For Object Y: [tex]\(32 \neq 3 \times 16\)[/tex]
- For Object Z: [tex]\(24 = 3 \times 8\)[/tex]
Therefore, Object [tex]\(Z\)[/tex] is the one whose distance is three times its displacement. The answer is [tex]\(Z\)[/tex].
