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Sagot :
Let's break down Meg's movement step by step to understand both her total distance traveled and her displacement.
1. First Leg of the Journey:
- Meg walks from her desk to the teacher's desk, which is a distance of [tex]\(2 \, \text{meters}\)[/tex].
2. Second Leg of the Journey:
- From the teacher's desk, Meg walks [tex]\(4 \, \text{meters}\)[/tex] in the opposite direction to the classroom door.
Total Distance Traveled:
- The total distance Meg travels is the sum of the distances of both legs of her journey.
- [tex]\[ \text{Total Distance} = 2 \, \text{meters} + 4 \, \text{meters} = 6 \, \text{meters} \][/tex]
Displacement:
- Displacement is a vector quantity, which means it has both magnitude and direction.
- Meg starts at her desk, walks [tex]\(2 \, \text{meters}\)[/tex] to the teacher's desk, then [tex]\(4 \, \text{meters}\)[/tex] in the opposite direction.
- Net displacement is determined by the final position relative to the starting point.
- Since she walked more towards the door, her displacement from the starting point is the difference between the two distances:
- [tex]\[ \text{Displacement} = 4 \, \text{meters} - 2 \, \text{meters} = 2 \, \text{meters} \text{ to the left} \][/tex]
Now let's look at the provided tables:
- Option A:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $2 m$ & $2 m$ to the left \\ \hline \end{tabular} \][/tex]
This option is incorrect because it lists the distance as [tex]\(2 \, \text{meters}\)[/tex] instead of the correct total distance of [tex]\(6 \, \text{meters}\)[/tex].
- Option B:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $6 m$ & $2 m$ to the left \\ \hline \end{tabular} \][/tex]
This option correctly lists the total distance as [tex]\(6 \, \text{meters}\)[/tex] and the displacement as [tex]\(2 \, \text{meters}\)[/tex] to the left, which matches our calculations.
- Option C:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $2 m$ & $6 m$ to the left \\ \hline \end{tabular} \][/tex]
This option is incorrect because both the distance and the displacement are incorrect.
- Option D:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $6 m$ & $6 m$ to the left \\ \hline \end{tabular} \][/tex]
This option is incorrect because it incorrectly lists the displacement as [tex]\(6 \, \text{meters}\)[/tex] to the left.
Therefore, the correct table is:
Option B:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $6 m$ & $2 m$ to the left \\ \hline \end{tabular} \][/tex]
1. First Leg of the Journey:
- Meg walks from her desk to the teacher's desk, which is a distance of [tex]\(2 \, \text{meters}\)[/tex].
2. Second Leg of the Journey:
- From the teacher's desk, Meg walks [tex]\(4 \, \text{meters}\)[/tex] in the opposite direction to the classroom door.
Total Distance Traveled:
- The total distance Meg travels is the sum of the distances of both legs of her journey.
- [tex]\[ \text{Total Distance} = 2 \, \text{meters} + 4 \, \text{meters} = 6 \, \text{meters} \][/tex]
Displacement:
- Displacement is a vector quantity, which means it has both magnitude and direction.
- Meg starts at her desk, walks [tex]\(2 \, \text{meters}\)[/tex] to the teacher's desk, then [tex]\(4 \, \text{meters}\)[/tex] in the opposite direction.
- Net displacement is determined by the final position relative to the starting point.
- Since she walked more towards the door, her displacement from the starting point is the difference between the two distances:
- [tex]\[ \text{Displacement} = 4 \, \text{meters} - 2 \, \text{meters} = 2 \, \text{meters} \text{ to the left} \][/tex]
Now let's look at the provided tables:
- Option A:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $2 m$ & $2 m$ to the left \\ \hline \end{tabular} \][/tex]
This option is incorrect because it lists the distance as [tex]\(2 \, \text{meters}\)[/tex] instead of the correct total distance of [tex]\(6 \, \text{meters}\)[/tex].
- Option B:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $6 m$ & $2 m$ to the left \\ \hline \end{tabular} \][/tex]
This option correctly lists the total distance as [tex]\(6 \, \text{meters}\)[/tex] and the displacement as [tex]\(2 \, \text{meters}\)[/tex] to the left, which matches our calculations.
- Option C:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $2 m$ & $6 m$ to the left \\ \hline \end{tabular} \][/tex]
This option is incorrect because both the distance and the displacement are incorrect.
- Option D:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $6 m$ & $6 m$ to the left \\ \hline \end{tabular} \][/tex]
This option is incorrect because it incorrectly lists the displacement as [tex]\(6 \, \text{meters}\)[/tex] to the left.
Therefore, the correct table is:
Option B:
[tex]\[ \begin{tabular}{|c|c|} \hline Distance & Displacement \\ \hline $6 m$ & $2 m$ to the left \\ \hline \end{tabular} \][/tex]
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