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Sagot :
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### Given Information:
- The businessman walks 5 meters East (from A to B).
- He then walks 7 meters West (from B to C).
- The total time taken for this journey is 20 seconds.
### Questions to Address:
1. Draw a vector scale diagram representing the two displacements.
2. Label all vectors clearly.
3. Write down the displacements next to the vectors using a scale of 1 cm representing 1 m.
### Step-by-Step Solution:
#### 1. Drawing the Vector Scale Diagram:
Since 1 cm on the diagram represents 1 meter, you can use a ruler to be accurate.
From A to B:
- Draw a straight horizontal line towards the right (East direction).
- Label the starting point as A.
- This line should be 5 cm long (because 5 meters scaled down by 1:1 is 5 cm).
- Label the endpoint of this line as B.
- Next to this line, write "5 meters East."
From B to C:
- From point B, draw another straight horizontal line towards the left (West direction).
- This line should be 7 cm long (because 7 meters scaled down by 1:1 is 7 cm).
- Label the endpoint of this line as C.
- Next to this line, write "7 meters West."
Here is a textual representation of the diagram:
```
A -----(5 cm)----> B <-------(7 cm)------ C
| | |
5m East 7m West
```
### Result Details
- The net displacement (total displacement with direction considered), total distance traveled, and average speed:
1. Total Displacement:
- From A to B: 5 meters East.
- From B to C: 7 meters West.
- Since East is considered positive and West negative, the displacement from B to C is -7 meters.
- Therefore, total displacement = [tex]\(5 \, meters + (-7 \, meters) = -2 \, meters\)[/tex].
- The negative sign indicates the final displacement is 2 meters to the West.
2. Average Velocity:
- Total displacement is -2 meters.
- Time taken is 20 seconds.
- Average velocity = [tex]\(\frac{\text{Total Displacement}}{\text{Time Taken}} = \frac{-2 \, \text{meters}}{20 \, \text{seconds}} = -0.1 \, \text{meters/second}\)[/tex].
- The negative sign indicates the direction is West.
3. Total Distance Traveled:
- Distance from A to B is 5 meters.
- Distance from B to C is 7 meters.
- Total distance traveled = [tex]\(5 + 7 = 12 \, \text{meters}\)[/tex].
4. Average Speed:
- Total distance traveled is 12 meters.
- Time taken is 20 seconds.
- Average speed = [tex]\(\frac{\text{Total Distance Travelled}}{\text{Time Taken}} = \frac{12 \, \text{meters}}{20 \, \text{seconds}} = 0.6 \, \text{meters/second}\)[/tex].
So, the final figures are:
- Total Displacement: -2 meters
- Average Velocity: -0.1 meters/second
- Total Distance Traveled: 12 meters
- Average Speed: 0.6 meters/second
### Given Information:
- The businessman walks 5 meters East (from A to B).
- He then walks 7 meters West (from B to C).
- The total time taken for this journey is 20 seconds.
### Questions to Address:
1. Draw a vector scale diagram representing the two displacements.
2. Label all vectors clearly.
3. Write down the displacements next to the vectors using a scale of 1 cm representing 1 m.
### Step-by-Step Solution:
#### 1. Drawing the Vector Scale Diagram:
Since 1 cm on the diagram represents 1 meter, you can use a ruler to be accurate.
From A to B:
- Draw a straight horizontal line towards the right (East direction).
- Label the starting point as A.
- This line should be 5 cm long (because 5 meters scaled down by 1:1 is 5 cm).
- Label the endpoint of this line as B.
- Next to this line, write "5 meters East."
From B to C:
- From point B, draw another straight horizontal line towards the left (West direction).
- This line should be 7 cm long (because 7 meters scaled down by 1:1 is 7 cm).
- Label the endpoint of this line as C.
- Next to this line, write "7 meters West."
Here is a textual representation of the diagram:
```
A -----(5 cm)----> B <-------(7 cm)------ C
| | |
5m East 7m West
```
### Result Details
- The net displacement (total displacement with direction considered), total distance traveled, and average speed:
1. Total Displacement:
- From A to B: 5 meters East.
- From B to C: 7 meters West.
- Since East is considered positive and West negative, the displacement from B to C is -7 meters.
- Therefore, total displacement = [tex]\(5 \, meters + (-7 \, meters) = -2 \, meters\)[/tex].
- The negative sign indicates the final displacement is 2 meters to the West.
2. Average Velocity:
- Total displacement is -2 meters.
- Time taken is 20 seconds.
- Average velocity = [tex]\(\frac{\text{Total Displacement}}{\text{Time Taken}} = \frac{-2 \, \text{meters}}{20 \, \text{seconds}} = -0.1 \, \text{meters/second}\)[/tex].
- The negative sign indicates the direction is West.
3. Total Distance Traveled:
- Distance from A to B is 5 meters.
- Distance from B to C is 7 meters.
- Total distance traveled = [tex]\(5 + 7 = 12 \, \text{meters}\)[/tex].
4. Average Speed:
- Total distance traveled is 12 meters.
- Time taken is 20 seconds.
- Average speed = [tex]\(\frac{\text{Total Distance Travelled}}{\text{Time Taken}} = \frac{12 \, \text{meters}}{20 \, \text{seconds}} = 0.6 \, \text{meters/second}\)[/tex].
So, the final figures are:
- Total Displacement: -2 meters
- Average Velocity: -0.1 meters/second
- Total Distance Traveled: 12 meters
- Average Speed: 0.6 meters/second
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