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

\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.



Answer :

To determine which statements are supported by the information provided in the table, we need to calculate the kinetic energy for each student using the formula for kinetic energy:

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

Let's break this down step by step for each student:

1. Autumn:
- Mass = 50 kg
- Velocity = 4 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Autumn}} = \frac{1}{2} \times 50 \times (4)^2 = \frac{1}{2} \times 50 \times 16 = 0.5 \times 50 \times 16 = 400\, \text{Joules} \][/tex]

2. Mohammed:
- Mass = 57 kg
- Velocity = 3 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Mohammed}} = \frac{1}{2} \times 57 \times (3)^2 = \frac{1}{2} \times 57 \times 9 = 0.5 \times 57 \times 9 = 256.5\, \text{Joules} \][/tex]

3. Lexy:
- Mass = 53 kg
- Velocity = 2 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Lexy}} = \frac{1}{2} \times 53 \times (2)^2 = \frac{1}{2} \times 53 \times 4 = 0.5 \times 53 \times 4 = 106\, \text{Joules} \][/tex]

4. Chiang:
- Mass = 64 kg
- Velocity = 5 m/s
- Kinetic Energy: [tex]\[ KE_{\text{Chiang}} = \frac{1}{2} \times 64 \times (5)^2 = \frac{1}{2} \times 64 \times 25 = 0.5 \times 64 \times 25 = 800\, \text{Joules} \][/tex]

The resulting kinetic energies are:
- Autumn: 400 Joules
- Mohammed: 256.5 Joules
- Lexy: 106 Joules
- Chiang: 800 Joules

Now, let's evaluate each statement:

1. Autumn has more kinetic energy than Chiang.
- False. Autumn has 400 Joules, while Chiang has 800 Joules.

2. Mohammed has less kinetic energy than Autumn.
- True. Mohammed has 256.5 Joules, while Autumn has 400 Joules.

3. Lexy has more kinetic energy than Mohammed.
- False. Lexy has 106 Joules, while Mohammed has 256.5 Joules.

4. Chiang has less kinetic energy than Lexy.
- False. Chiang has 800 Joules, while Lexy has 106 Joules.

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