A watt is

Options

A. `(kgm)/(s^2)`
B. `kgm^2)/(s^3)`
C. `kg(m)/(s)`
D. `kg(m^2)/(s^2)`

Explanation

To find out what a watt is, we will break down the concept of power and its relation to work and time.

### Step-by-Step Solution:

1. **Definition of Watt**: A watt (W) is defined as the unit of power in the International System of Units (SI).

2. **Understanding Power**: Power is defined as the rate at which work is done. Mathematically, it can be expressed as:
\[ \text{Power} = \frac{\text{Work Done}}{\text{Time}} \]

3. **Work Done**: Work done (W) can be expressed in terms of force (F) and displacement (s):
\[ \text{Work Done} = \text{Force} \times \text{Displacement} = F \cdot s \]

4. **Force in Terms of Mass and Acceleration**: Force can be defined using Newton's second law, where force is the product of mass (m) and acceleration (a):
\[ F = m \cdot a \]

5. **Acceleration**: Acceleration (a) can be defined as the change in velocity over time, which can also be expressed as distance per time squared:
\[ a = \frac{s}{t^2} \]

6. **Combining the Equations**: Now substituting the expression for force into the work done equation:
\[ \text{Work Done} = (m \cdot a) \cdot s = m \cdot \left(\frac{s}{t^2}\right) \cdot s = \frac{m \cdot s^2}{t^2} \]

7. **Substituting Work Done into Power**: Now substituting work done back into the power equation:
\[ \text{Power} = \frac{\text{Work Done}}{t} = \frac{\frac{m \cdot s^2}{t^2}}{t} = \frac{m \cdot s^2}{t^3} \]

8. **Units of Power**: The units of power (watt) can now be expressed in terms of the base SI units:
- Mass (m) is measured in kilograms (kg)
- Displacement (s) is measured in meters (m)
- Time (t) is measured in seconds (s)

Therefore, the unit of power (watt) is:
\[ \text{Watt} = \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3} \]

9. **Conclusion**: Thus, a watt is defined as:
\[ 1 \text{ W} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3} \]