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.
