To determine which object has the greatest acceleration, we will use Newton's Second Law of Motion, [tex]\( F = ma \)[/tex], which can be rearranged to find acceleration [tex]\( a \)[/tex] as [tex]\( a = \frac{F}{m} \)[/tex].
Let's go step-by-step through each object:
1. Object 1
- Mass [tex]\( m = 10 \, \text{kg} \)[/tex]
- Force [tex]\( F = 4 \, \text{N} \)[/tex]
- Acceleration [tex]\( a = \frac{F}{m} = \frac{4 \, \text{N}}{10 \, \text{kg}} = 0.4 \, \text{m/s}^2 \)[/tex]
2. Object 2
- Mass [tex]\( m = 100 \, \text{g} = 0.1 \, \text{kg} \)[/tex] (since 1 kg = 1000 g)
- Force [tex]\( F = 20 \, \text{N} \)[/tex]
- Acceleration [tex]\( a = \frac{F}{m} = \frac{20 \, \text{N}}{0.1 \, \text{kg}} = 200 \, \text{m/s}^2 \)[/tex]
3. Object 3
- Mass [tex]\( m = 10 \, \text{g} = 0.01 \, \text{kg} \)[/tex]
- Force [tex]\( F = 4 \, \text{N} \)[/tex]
- Acceleration [tex]\( a = \frac{F}{m} = \frac{4 \, \text{N}}{0.01 \, \text{kg}} = 400 \, \text{m/s}^2 \)[/tex]
4. Object 4
- Mass [tex]\( m = 1 \, \text{kg} \)[/tex]
- Force [tex]\( F = 20 \, \text{N} \)[/tex]
- Acceleration [tex]\( a = \frac{F}{m} = \frac{20 \, \text{N}}{1 \, \text{kg}} = 20 \, \text{m/s}^2 \)[/tex]
Now, we compare the accelerations calculated for each object:
- 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].
Therefore, the correct answer is:
- Object 3
