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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|}{ Velocity (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 :

GinnyAnswer
To determine which statements are supported by the information in the chart, we need to calculate the kinetic energy (KE) for each student. The formula for kinetic energy is:

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

Let's compute the kinetic energy for each student step-by-step.

1. Kinetic Energy for Autumn:
- Mass = 50 kg
- Velocity = 4 m/s
[tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times 4^2 \][/tex]
[tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times 16 \][/tex]
[tex]\[ KE_{\text{Autumn}} = 25 \times 16 \][/tex]
[tex]\[ KE_{\text{Autumn}} = 400 \, \text{Joules} \][/tex]

2. Kinetic Energy for Mohammed:
- Mass = 57 kg
- Velocity = 3 m/s
[tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times 3^2 \][/tex]
[tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times 9 \][/tex]
[tex]\[ KE_{\text{Mohammed}} = 28.5 \times 9 \][/tex]
[tex]\[ KE_{\text{Mohammed}} = 256.5 \, \text{Joules} \][/tex]

3. Kinetic Energy for Lexy:
- Mass = 53 kg
- Velocity = 2 m/s
[tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times 2^2 \][/tex]
[tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times 4 \][/tex]
[tex]\[ KE_{\text{Lexy}} = 26.5 \times 4 \][/tex]
[tex]\[ KE_{\text{Lexy}} = 106 \, \text{Joules} \][/tex]

4. Kinetic Energy for Chiang:
- Mass = 64 kg
- Velocity = 5 m/s
[tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times 5^2 \][/tex]
[tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times 25 \][/tex]
[tex]\[ KE_{\text{Chiang}} = 32 \times 25 \][/tex]
[tex]\[ KE_{\text{Chiang}} = 800 \, \text{Joules} \][/tex]

Now that we have the kinetic energies:
- KE_{\text{Autumn}} = 400 \, \text{Joules}
- KE_{\text{Mohammed}} = 256.5 \, \text{Joules}
- KE_{\text{Lexy}} = 106 \, \text{Joules}
- KE_{\text{Chiang}} = 800 \, \text{Joules}

Let's evaluate each statement:

1. "Autumn has more kinetic energy than Chiang."
- 400 Joules (Autumn) is less than 800 Joules (Chiang).
- This statement is False.

2. "Mohammed has less kinetic energy than Autumn."
- 256.5 Joules (Mohammed) is less than 400 Joules (Autumn).
- This statement is True.

3. "Lexy has more kinetic energy than Mohammed."
- 106 Joules (Lexy) is less than 256.5 Joules (Mohammed).
- This statement is False.

4. "Chiang has less kinetic energy than Lexy."
- 800 Joules (Chiang) is greater than 106 Joules (Lexy).
- This statement is False.

Therefore, the only statement supported by the information is:
- Mohammed has less kinetic energy than Autumn.
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