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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 provided in the table, let's analyze the kinetic energy of each student. Kinetic energy (KE) is given by the formula:

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

From the table, we have the mass and velocity of each student.

1. Calculate the kinetic energy for each student:

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

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

- Lexy:
[tex]\[ \text{mass} = 53 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 2 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times (2)^2 = \frac{1}{2} \times 53 \times 4 = 106 \, \text{J} \][/tex]

- Chiang:
[tex]\[ \text{mass} = 64 \, \text{kg} \][/tex]
[tex]\[ \text{velocity} = 5 \, \text{m/s} \][/tex]
[tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times (5)^2 = \frac{1}{2} \times 64 \times 25 = 800 \, \text{J} \][/tex]

2. Evaluate each statement:

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

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

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

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

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