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The table shows information about four students who are running around a track.

Motion of Students

\begin{tabular}{|l|l|l|}
\hline \multicolumn{1}{|c|}{ Student Name } & \multicolumn{1}{|c|}{ Mass (kg) } & \multicolumn{1}{|c|}{ Speed (m/s) } \\
\hline Autumn & 50 & 4 \\
\hline Mohammed & 57 & 3 \\
\hline Lexy & 53 & 2 \\
\hline Chiang & 64 & 5 \\
\hline
\end{tabular}

Which statement is supported by the information in the chart?

A. Autumn has more kinetic energy than Chiang.
B. Mohammed has less kinetic energy than Autumn.
C. Lexy has more kinetic energy than Mohammed.
D. Chiang has less kinetic energy than Lexy.

Sagot :

GinnyAnsweridn
To solve this problem, we need to calculate the kinetic energy of each student. The formula for kinetic energy (KE) is given by:

[tex]\[ KE = \frac{1}{2} \times \text{mass} \times \text{speed}^2 \][/tex]

We'll use this formula for each student.

### Calculations

1. Autumn:
- Mass: 50 kg
- Speed: 4 m/s
- Kinetic Energy: [tex]\( KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times 4^2 = \frac{1}{2} \times 50 \times 16 = 400 \, \text{J} \)[/tex]

2. Mohammed:
- Mass: 57 kg
- Speed: 3 m/s
- Kinetic Energy: [tex]\( KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times 3^2 = \frac{1}{2} \times 57 \times 9 = 256.5 \, \text{J} \)[/tex]

3. Lexy:
- Mass: 53 kg
- Speed: 2 m/s
- Kinetic Energy: [tex]\( KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times 2^2 = \frac{1}{2} \times 53 \times 4 = 106 \, \text{J} \)[/tex]

4. Chiang:
- Mass: 64 kg
- Speed: 5 m/s
- Kinetic Energy: [tex]\( KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times 5^2 = \frac{1}{2} \times 64 \times 25 = 800 \, \text{J} \)[/tex]

### Evaluating Statements:

1. Autumn has more kinetic energy than Chiang.
- [tex]\( KE_{\text{Autumn}} = 400 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Chiang}} = 800 \, \text{J} \)[/tex]
- [tex]\( 400 \text{ J} < 800 \text{ J} \)[/tex], so this statement is False.

2. Mohammed has less kinetic energy than Autumn.
- [tex]\( KE_{\text{Mohammed}} = 256.5 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Autumn}} = 400 \, \text{J} \)[/tex]
- [tex]\( 256.5 \text{ J} < 400 \text{ J} \)[/tex], so this statement is True.

3. Lexy has more kinetic energy than Mohammed.
- [tex]\( KE_{\text{Lexy}} = 106 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Mohammed}} = 256.5 \, \text{J} \)[/tex]
- [tex]\( 106 \text{ J} < 256.5 \text{ J} \)[/tex], so this statement is False.

4. Chiang has less kinetic energy than Lexy.
- [tex]\( KE_{\text{Chiang}} = 800 \, \text{J} \)[/tex]
- [tex]\( KE_{\text{Lexy}} = 106 \, \text{J} \)[/tex]
- [tex]\( 800 \text{ J} > 106 \text{ J} \)[/tex], so this statement is False.

Based on these calculations, the statement supported by the information in the chart is:

"Mohammed has less kinetic energy than Autumn."
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