> [!summary] Kinetic energy is the amount of energy an object has because it's moving > **Key Equations:** > Kinetic energy: $K = \frac{1}{2}mv^2$ > Work-Energy Theorem: $W=\Delta K$ / $W = \Delta E$ >[!info]+ Read Time **⏱ 1 min** # Definiton Kinetic energy is how much energy an object has because it is moving. It's the [[Work|work]] done on an object to give it or keep it in motion ## Derivation (Work-Energy Theorem) > [!warning] Assumptions To derive an equation to describe the energy when a force gives an object motion, assume the following: > - [[Work|Work]] is general is $W = \int_{x_{i}}^{x_{f}} \vec{F} \cdot \vec{dx}$ > - The [[Forces|force]] is always constant > - Force is described as $F=ma$ > - The object has mass $m$ > - From [[Kinematics|kinematics]] $ax = \frac{1}{2}(v^2 - v_0 ^2)$ $\begin{array}{c} W = \int_{x_{i}}^{x_{f}} \vec{F} \cdot \vec{dx}\\ W = F\Delta x \\ W = ma\Delta x \\ W = \frac{1}{2}m (v^2 - v_0 ^2) \\ \\ \text{So the kinetic energy can be described as:} \\ \Delta K = \frac{1}{2}m (v^2 - v_0 ^2) \\ \\ \text{Then we make the defintion of a work-energy theorem:} \\ W = \Delta K \\ \end{array}$ > [!note] $W =\Delta K$ is valid for any type of energy $W = \Delta E$ --- > ✍️ This project’s been a labour of love. > If it helped, [give Math & Matter a star](https://github.com/rajeevphysics/Obsidian-MathMatter) and let me know what you'd like to see next. ---