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Four different objects are placed on a number line at 0. The chart describes the motion of each object:

\begin{tabular}{|l|l|}
\hline
Object & Motion \\
\hline
W & 3 units left, then 3 units right \\
\hline
X & 6 units right, then 18 units right \\
\hline
Y & 8 units left, then 24 units right \\
\hline
Z & 16 units right, then 8 units left \\
\hline
\end{tabular}

Using the information in the chart, determine the distance and displacement of each object. Which object has a distance that is three times as great as its displacement?

A. W
B. X
C. Y
D. Z



Answer :

GinnyAnswer
To solve the problem, we need to determine the distance and displacement for each object and check if the distance is three times the displacement for any of them.

1. Object W:
- Motion: 3 units left, then 3 units right.
- Distance calculation: [tex]\(3 + 3 = 6\)[/tex] units.
- Displacement calculation: [tex]\(-3 + 3 = 0\)[/tex] units.
- Does [tex]\(6 = 3 \times 0\)[/tex]? No.

2. Object X:
- Motion: 6 units right, then 18 units right.
- Distance calculation: [tex]\(6 + 18 = 24\)[/tex] units.
- Displacement calculation: [tex]\(6 + 18 = 24\)[/tex] units.
- Does [tex]\(24 = 3 \times 24\)[/tex]? No.

3. Object Y:
- Motion: 8 units left, then 24 units right.
- Distance calculation: [tex]\(8 + 24 = 32\)[/tex] units.
- Displacement calculation: [tex]\(-8 + 24 = 16\)[/tex] units.
- Does [tex]\(32 = 3 \times 16\)[/tex]? No.

4. Object Z:
- Motion: 16 units right, then 8 units left.
- Distance calculation: [tex]\(16 + 8 = 24\)[/tex] units.
- Displacement calculation: [tex]\(16 - 8 = 8\)[/tex] units.
- Does [tex]\(24 = 3 \times 8\)[/tex]? Yes.

Therefore, the object that has a distance three times as great as its displacement is [tex]\( \boxed{Z} \)[/tex].

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