Work-Energy Theorem

📊 intermediate

$$W = \Delta K = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$

The work done by the net force on a particle equals the change in its kinetic energy.

Variables & Units

$W$

Work Done

Unit: Joule ($J$)

$\Delta K$

Change in Kinetic Energy

Unit: Joule ($J$)

$v_f, v_i$

Final and Initial velocities

Unit: $m/s$

Key Information

📐 Derived From

Integration of Newton's Second Law with respect to displacement.

💡 Example

Work needed to stop a car moving at speed $v$.

🔧 Applications

Mechanical engineering and sports science.

⚠️ Constraints

Assumes a rigid body or point particle.

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