Answered

Luis and Aisha conducted an experiment. They exerted different forces on four objects. Their results are shown in the table.

\begin{tabular}{|c|c|c|}
\hline
Object & Mass & Force (N) \\
\hline
1 & 10 kg & 4 N \\
\hline
2 & 100 g & 20 N \\
\hline
3 & 10 g & 4 N \\
\hline
4 & 1 kg & 20 N \\
\hline
\end{tabular}

Based on the data, which object has the greatest acceleration?

A. Object 1
B. Object 2
C. Object 3
D. Object 4



Answer :

GinnyAnswer
To determine which object has the greatest acceleration, we will use Newton's second law, which states that the acceleration ([tex]\( a \)[/tex]) of an object is given by the net force ([tex]\( F \)[/tex]) acting on it divided by its mass ([tex]\( m \)[/tex]):

[tex]\[ a = \frac{F}{m} \][/tex]

Let's calculate the acceleration for each object based on the given data.

### Object 1:
- Mass: [tex]\( 10 \ \text{kg} \)[/tex]
- Force: [tex]\( 4 \ \text{N} \)[/tex]

[tex]\[ a_1 = \frac{4 \ \text{N}}{10 \ \text{kg}} = 0.4 \ \text{m/s}^2 \][/tex]

### Object 2:
- Mass: [tex]\( 100 \ \text{g} = 0.1 \ \text{kg} \)[/tex] (Note: 1 kg = 1000 g)
- Force: [tex]\( 20 \ \text{N} \)[/tex]

[tex]\[ a_2 = \frac{20 \ \text{N}}{0.1 \ \text{kg}} = 200 \ \text{m/s}^2 \][/tex]

### Object 3:
- Mass: [tex]\( 10 \ \text{g} = 0.01 \ \text{kg} \)[/tex]
- Force: [tex]\( 4 \ \text{N} \)[/tex]

[tex]\[ a_3 = \frac{4 \ \text{N}}{0.01 \ \text{kg}} = 400 \ \text{m/s}^2 \][/tex]

### Object 4:
- Mass: [tex]\( 1 \ \text{kg} \)[/tex]
- Force: [tex]\( 20 \ \text{N} \)[/tex]

[tex]\[ a_4 = \frac{20 \ \text{N}}{1 \ \text{kg}} = 20 \ \text{m/s}^2 \][/tex]

### Comparing Accelerations:
- Object 1: [tex]\( 0.4 \ \text{m/s}^2 \)[/tex]
- Object 2: [tex]\( 200 \ \text{m/s}^2 \)[/tex]
- Object 3: [tex]\( 400 \ \text{m/s}^2 \)[/tex]
- Object 4: [tex]\( 20 \ \text{m/s}^2 \)[/tex]

The object with the greatest acceleration is Object 3 with an acceleration of [tex]\( 400 \ \text{m/s}^2 \)[/tex].

Conclusion: Based on the data, Object 3 has the greatest acceleration.

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