To determine which of the given statements are supported by the information presented, we need to calculate the kinetic energy for each student using the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( v \)[/tex] is the velocity.
Here are the mass and velocity values for all students:
- Autumn: mass = 50 kg, velocity = 4 m/s
- Mohammed: mass = 57 kg, velocity = 3 m/s
- Lexy: mass = 53 kg, velocity = 2 m/s
- Chiang: mass = 64 kg, velocity = 5 m/s
Now we calculate the kinetic energy for each student:
1. Autumn's Kinetic Energy:
[tex]\[ KE_{Autumn} = \frac{1}{2} \times 50 \times (4)^2 = \frac{1}{2} \times 50 \times 16 = 0.5 \times 800 = 400.0 \, \text{Joules} \][/tex]
2. Mohammed's Kinetic Energy:
[tex]\[ KE_{Mohammed} = \frac{1}{2} \times 57 \times (3)^2 = \frac{1}{2} \times 57 \times 9 = 0.5 \times 513 = 256.5 \, \text{Joules} \][/tex]
3. Lexy's Kinetic Energy:
[tex]\[ KE_{Lexy} = \frac{1}{2} \times 53 \times (2)^2 = \frac{1}{2} \times 53 \times 4 = 0.5 \times 212 = 106.0 \, \text{Joules} \][/tex]
4. Chiang's Kinetic Energy:
[tex]\[ KE_{Chiang} = \frac{1}{2} \times 64 \times (5)^2 = \frac{1}{2} \times 64 \times 25 = 0.5 \times 1600 = 800.0 \, \text{Joules} \][/tex]
Now, let's evaluate each statement based on these kinetic energies:
1. Autumn has more kinetic energy than Chiang.
[tex]\[ 400.0 \, \text{J} (Autumn) < 800.0 \, \text{J} (Chiang) \][/tex]
This statement is False.
2. Mohammed has less kinetic energy than Autumn.
[tex]\[ 256.5 \, \text{J} (Mohammed) < 400.0 \, \text{J} (Autumn) \][/tex]
This statement is True.
3. Lexy has more kinetic energy than Mohammed.
[tex]\[ 106.0 \, \text{J} (Lexy) < 256.5 \, \text{J} (Mohammed) \][/tex]
This statement is False.
4. Chiang has less kinetic energy than Lexy.
[tex]\[ 800.0 \, \text{J} (Chiang) > 106.0 \, \text{J} (Lexy) \][/tex]
This statement is False.
So, the correct statement supported by the information in the chart is:
- Mohammed has less kinetic energy than Autumn.
