Question
The table shows information about four students who are running around a track.
A 3-column table with 4 rows titled Motion of Students. The first column labeled Student name has entries Autumn, MOhammed, Lexy, Chiang. The second column labeled Mass (kilograms) has entries 50, 57, 53, 64. The third column labeled Velocity (meters per second) has entries 4, 3, 2, 5.
Which statement is supported by the information in the chart?
Autumn has more kinetic energy than Chiang.
Mohammed has less kinetic energy than Autumn.
Lexy has more kinetic energy than Mohammed.
Chiang has less kinetic energy than Lexy.
A 3-column table with 4 rows titled Motion of Students. The first column labeled Student name has entries Autumn, MOhammed, Lexy, Chiang. The second column labeled Mass (kilograms) has entries 50, 57, 53, 64. The third column labeled Velocity (meters per second) has entries 4, 3, 2, 5.
Which statement is supported by the information in the chart?
Autumn has more kinetic energy than Chiang.
Mohammed has less kinetic energy than Autumn.
Lexy has more kinetic energy than Mohammed.
Chiang has less kinetic energy than Lexy.
Answers
GPT-4o mini
To determine which statement is supported by the information in the chart, we first need to calculate the kinetic energy for each student using the formula for kinetic energy:
\[ KE = \frac{1}{2} mv^2 \]
where \( KE \) is the kinetic energy, \( m \) is the mass, and \( v \) is the velocity.
Let's calculate the kinetic energy for each student:
1. **Autumn**:
- Mass = 50 kg
- Velocity = 4 m/s
- \( KE = \frac{1}{2} \cdot 50 \cdot (4)^2 = 25 \cdot 16 = 400 \) joules
2. **Mohammed**:
- Mass = 57 kg
- Velocity = 3 m/s
- \( KE = \frac{1}{2} \cdot 57 \cdot (3)^2 = 28.5 \cdot 9 = 256.5 \) joules
3. **Lexy**:
- Mass = 53 kg
- Velocity = 2 m/s
- \( KE = \frac{1}{2} \cdot 53 \cdot (2)^2 = 26.5 \cdot 4 = 106 \) joules
4. **Chiang**:
- Mass = 64 kg
- Velocity = 5 m/s
- \( KE = \frac{1}{2} \cdot 64 \cdot (5)^2 = 32 \cdot 25 = 800 \) joules
Now we can compare the kinetic energies:
- Autumn: 400 joules
- Mohammed: 256.5 joules
- Lexy: 106 joules
- Chiang: 800 joules
Now we can evaluate each statement:
1. **Autumn has more kinetic energy than Chiang.**
- False (400 < 800)
2. **Mohammed has less kinetic energy than Autumn.**
- True (256.5 < 400)
3. **Lexy has more kinetic energy than Mohammed.**
- False (106 < 256.5)
4. **Chiang has less kinetic energy than Lexy.**
- False (800 > 106)
The only statement supported by the information in the chart is:
**Mohammed has less kinetic energy than Autumn.**
\[ KE = \frac{1}{2} mv^2 \]
where \( KE \) is the kinetic energy, \( m \) is the mass, and \( v \) is the velocity.
Let's calculate the kinetic energy for each student:
1. **Autumn**:
- Mass = 50 kg
- Velocity = 4 m/s
- \( KE = \frac{1}{2} \cdot 50 \cdot (4)^2 = 25 \cdot 16 = 400 \) joules
2. **Mohammed**:
- Mass = 57 kg
- Velocity = 3 m/s
- \( KE = \frac{1}{2} \cdot 57 \cdot (3)^2 = 28.5 \cdot 9 = 256.5 \) joules
3. **Lexy**:
- Mass = 53 kg
- Velocity = 2 m/s
- \( KE = \frac{1}{2} \cdot 53 \cdot (2)^2 = 26.5 \cdot 4 = 106 \) joules
4. **Chiang**:
- Mass = 64 kg
- Velocity = 5 m/s
- \( KE = \frac{1}{2} \cdot 64 \cdot (5)^2 = 32 \cdot 25 = 800 \) joules
Now we can compare the kinetic energies:
- Autumn: 400 joules
- Mohammed: 256.5 joules
- Lexy: 106 joules
- Chiang: 800 joules
Now we can evaluate each statement:
1. **Autumn has more kinetic energy than Chiang.**
- False (400 < 800)
2. **Mohammed has less kinetic energy than Autumn.**
- True (256.5 < 400)
3. **Lexy has more kinetic energy than Mohammed.**
- False (106 < 256.5)
4. **Chiang has less kinetic energy than Lexy.**
- False (800 > 106)
The only statement supported by the information in the chart is:
**Mohammed has less kinetic energy than Autumn.**