The Theorem of Kinetic Energy, also known as the Work-Energy Theorem, is a fundamental principle in physics that relates the work done on an object to its change in kinetic energy. It states that the net work done on an object is equal to the change in its kinetic energy.

The Theorem of Kinetic Energy is expressed by the following equation:

\[ W = \Delta KE = \frac{1}{2}m(v_2^2 - v_1^2) \]

Where:

- \(W\) is the work done on the object (measured in joules, J)
- \(\Delta KE\) is the change in kinetic energy (measured in joules, J)
- \(m\) is the mass of the object (measured in kilograms, kg)
- \(v_1\) is the initial velocity of the object (measured in meters per second, m/s)
- \(v_2\) is the final velocity of the object (measured in meters per second, m/s)

Let's calculate the work done on a 1000 kg car accelerating from 0 m/s to 20 m/s:

- Identify the known values:
- Mass (m) = 1000 kg
- Initial velocity (v₁) = 0 m/s
- Final velocity (v₂) = 20 m/s

- Apply the Theorem of Kinetic Energy formula: \[ W = \frac{1}{2}m(v_2^2 - v_1^2) \]
- Substitute the known values: \[ W = \frac{1}{2} \cdot 1000 \cdot (20^2 - 0^2) \]
- Perform the calculation: \[ W = \frac{1}{2} \cdot 1000 \cdot (400 - 0) = 200,000 \text{ J} \]

Let's visualize the Theorem of Kinetic Energy with our example:

This visual representation shows:

- The initial state of the car (v₁ = 0 m/s)
- The final state of the car (v₂ = 20 m/s)
- The work done on the car (200,000 J), which is equal to the change in kinetic energy
- The mass of the car (1000 kg)

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