To solve the question regarding the unit \( N \, \text{kg}^{-1} \), we will analyze the components of the unit and relate them to the physical quantities they represent.
### Step-by-Step Solution:
1. **Understanding the Unit**:
The unit given is \( N \, \text{kg}^{-1} \). Here, \( N \) stands for Newton, which is the unit of force, and \( \text{kg} \) stands for kilogram, which is the unit of mass.
2. **Breaking Down the Units**:
We know that:
\[
1 \, N = 1 \, \text{kg} \cdot \text{m/s}^2
\]
This means that a Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
3. **Expressing \( N \, \text{kg}^{-1} \)**:
Now, we can express \( N \, \text{kg}^{-1} \) as:
\[
N \, \text{kg}^{-1} = \frac{1 \, N}{1 \, \text{kg}} = \frac{1 \, \text{kg} \cdot \text{m/s}^2}{1 \, \text{kg}}
\]
Here, the kilograms in the numerator and denominator cancel out:
\[
N \, \text{kg}^{-1} = \text{m/s}^2
\]
4. **Identifying the Quantity**:
The unit \( \text{m/s}^2 \) is the unit of acceleration. Therefore, \( N \, \text{kg}^{-1} \) is the unit of acceleration.
5. **Conclusion**:
Based on the analysis, the correct answer to the question is that \( N \, \text{kg}^{-1} \) is the unit of acceleration.
### Final Answer:
The unit \( N \, \text{kg}^{-1} \) is the unit of **acceleration**.
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