Question
A ball travels at a constant speed of 6 meters per second along a frictionless surface. Which table correctly shows what a student may have measured and recorded if they watched this ball in motion over a 10-second time period?
A.
Time (seconds) Distance (meters)
2 12
4 24
6 36
8 48
10 60
B.
Time (seconds) Distance (meters)
2 6
4 12
6 24
8 36
10 42
C.
Time (seconds) Distance (meters)
2 24
4 34
6 44
8 54
10 64
D.
Time (seconds) Distance (meters)
2 12
4 20
6 22
8 30
10 32
A.
Time (seconds) Distance (meters)
2 12
4 24
6 36
8 48
10 60
B.
Time (seconds) Distance (meters)
2 6
4 12
6 24
8 36
10 42
C.
Time (seconds) Distance (meters)
2 24
4 34
6 44
8 54
10 64
D.
Time (seconds) Distance (meters)
2 12
4 20
6 22
8 30
10 32
Answers
GPT-4o mini
To find the correct table of measurements, we can use the relationship between speed, distance, and time. The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
In this case, the speed of the ball is 6 meters per second. We can calculate the distance traveled at various time intervals:
- At 2 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 2 \, \text{s} = 12 \, \text{meters} \]
- At 4 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 4 \, \text{s} = 24 \, \text{meters} \]
- At 6 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 6 \, \text{s} = 36 \, \text{meters} \]
- At 8 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 8 \, \text{s} = 48 \, \text{meters} \]
- At 10 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 10 \, \text{s} = 60 \, \text{meters} \]
Now we can check each of the given tables against these calculations:
**A.**
Time (seconds) | Distance (meters)
----------------|--------------------
2 | 12
4 | 24
6 | 36
8 | 48
10 | 60
This table matches perfectly with our calculations.
**B.**
Time (seconds) | Distance (meters)
----------------|--------------------
2 | 6
4 | 12
6 | 24
8 | 36
10 | 42
This table does not match.
**C.**
Time (seconds) | Distance (meters)
----------------|--------------------
2 | 24
4 | 34
6 | 44
8 | 54
10 | 64
This table does not match.
**D.**
Time (seconds) | Distance (meters)
----------------|--------------------
2 | 12
4 | 20
6 | 22
8 | 30
10 | 32
This table does not match.
The only table that matches the expected results is Table **A**.
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
In this case, the speed of the ball is 6 meters per second. We can calculate the distance traveled at various time intervals:
- At 2 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 2 \, \text{s} = 12 \, \text{meters} \]
- At 4 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 4 \, \text{s} = 24 \, \text{meters} \]
- At 6 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 6 \, \text{s} = 36 \, \text{meters} \]
- At 8 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 8 \, \text{s} = 48 \, \text{meters} \]
- At 10 seconds:
\[ \text{Distance} = 6 \, \text{m/s} \times 10 \, \text{s} = 60 \, \text{meters} \]
Now we can check each of the given tables against these calculations:
**A.**
Time (seconds) | Distance (meters)
----------------|--------------------
2 | 12
4 | 24
6 | 36
8 | 48
10 | 60
This table matches perfectly with our calculations.
**B.**
Time (seconds) | Distance (meters)
----------------|--------------------
2 | 6
4 | 12
6 | 24
8 | 36
10 | 42
This table does not match.
**C.**
Time (seconds) | Distance (meters)
----------------|--------------------
2 | 24
4 | 34
6 | 44
8 | 54
10 | 64
This table does not match.
**D.**
Time (seconds) | Distance (meters)
----------------|--------------------
2 | 12
4 | 20
6 | 22
8 | 30
10 | 32
This table does not match.
The only table that matches the expected results is Table **A**.