kg `m^(2) s^(-2)` represents the unit of

Options

A. kinetic energy only
B. work done only
C. potential energy only
D. all the above

Answer

To determine what the unit \( \text{kg m}^2 \text{s}^{-2} \) represents, we will analyze it step by step by looking at the physical quantities associated with this unit.

### Step 1: Understanding the Unit
The unit \( \text{kg m}^2 \text{s}^{-2} \) can be broken down into its components:
- \( \text{kg} \) represents mass.
- \( \text{m}^2 \) represents area (since it is meter squared).
- \( \text{s}^{-2} \) represents acceleration (since it is the inverse of time squared).

### Step 2: Kinetic Energy
The formula for kinetic energy (\( KE \)) is:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( m \) is mass in kg.
- \( v \) is velocity in m/s.

To find the unit of kinetic energy:
\[ \text{Unit of } KE = \text{kg} \cdot \left(\text{m/s}\right)^2 = \text{kg} \cdot \frac{\text{m}^2}{\text{s}^2} = \text{kg m}^2 \text{s}^{-2} \]
Thus, the unit \( \text{kg m}^2 \text{s}^{-2} \) represents kinetic energy.

### Step 3: Work Done
The formula for work done (\( W \)) is:
\[ W = F \cdot d \]
Where:
- \( F \) is force in Newtons (N).
- \( d \) is displacement in meters (m).

To find the unit of work done, we first express force:
\[ F = m \cdot a \]
Where \( a \) is acceleration in \( \text{m/s}^2 \). Therefore, the unit of force is:
\[ \text{N} = \text{kg} \cdot \text{m/s}^2 \]
Now substituting this back into the work done formula:
\[ \text{Unit of } W = \text{N} \cdot \text{m} = \left(\text{kg} \cdot \frac{\text{m}}{\text{s}^2}\right) \cdot \text{m} = \text{kg m}^2 \text{s}^{-2} \]
Thus, the unit \( \text{kg m}^2 \text{s}^{-2} \) also represents work done.

### Step 4: Potential Energy
The formula for potential energy (\( PE \)) is:
\[ PE = mgh \]
Where:
- \( m \) is mass in kg.
- \( g \) is acceleration due to gravity in \( \text{m/s}^2 \).
- \( h \) is height in meters (m).

To find the unit of potential energy:
\[ \text{Unit of } PE = \text{kg} \cdot \text{m/s}^2 \cdot \text{m} = \text{kg} \cdot \frac{\text{m}^2}{\text{s}^2} = \text{kg m}^2 \text{s}^{-2} \]
Thus, the unit \( \text{kg m}^2 \text{s}^{-2} \) also represents potential energy.

### Conclusion
Since the unit \( \text{kg m}^2 \text{s}^{-2} \) represents kinetic energy, work done, and potential energy, we conclude that it represents all of the above.

### Final Answer
The unit \( \text{kg m}^2 \text{s}^{-2} \) represents:
**All of the above (kinetic energy, work done, and potential energy).**

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