The unit N-s is equivalenl to

Options

A. J
B. `kg-m-s^(-1)`
C. `kg-m-s^(-2)`
D. N-m-s

Answer

To determine what the unit N-s (Newton-second) is equivalent to, we will analyze the options provided step by step.

### Step 1: Understanding Newton-second (N-s)
The unit N-s is a product of force (Newton) and time (second). Therefore, we can express it as:
\[ \text{N-s} = \text{Newton} \times \text{second} \]

### Step 2: Analyzing the options
We have four options to compare with N-s:
1. Joule (J)
2. kg·m/s (kilogram meter per second)
3. kg·m/s² (kilogram meter per second squared)
4. N·m·s (Newton meter second)

#### Option 1: Joule (J)
Joule is defined as the work done when a force of 1 Newton displaces an object by 1 meter. Therefore:
\[ 1 \text{ Joule} = 1 \text{ Newton} \times 1 \text{ meter} \]
This means:
\[ \text{J} = \text{N} \cdot \text{m} \]
Since N-s is not equal to J, we can eliminate this option.

#### Option 2: kg·m/s
This unit represents momentum. According to Newton's second law, momentum (p) is given by:
\[ p = m \cdot v \]
Where \( m \) is mass (kg) and \( v \) is velocity (m/s). Thus:
\[ \text{kg} \cdot \text{m/s} = \text{N-s} \]
This means N-s is equivalent to kg·m/s.

#### Option 3: kg·m/s²
This unit represents force (Newton). According to Newton's second law:
\[ F = m \cdot a \]
Where \( a \) is acceleration (m/s²). Thus:
\[ \text{kg} \cdot \text{m/s}^2 = \text{N} \]
This means N-s is not equal to kg·m/s², so we can eliminate this option.

#### Option 4: N·m·s
This unit is the product of force, distance, and time. It does not correspond to a single physical quantity like momentum or impulse. Therefore, it is not equivalent to N-s.

### Conclusion
After analyzing all the options, we find that the correct equivalence for N-s is:
\[ \text{N-s} = \text{kg} \cdot \text{m/s} \]
Thus, the answer is **Option 2: kg·m/s**.

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