Kinetic Potential Energy & Work-Energy Theorem

Summary

Kinetic energy is the amount of energy an object has because it's moving

Key Equations:

Kinetic energy:
$K = \frac{1}{2} m v^{2}$

Work-Energy Theorem:
$W = Δ K$ / $W = Δ E$

Read Time

⏱ 1 min

Definiton

Kinetic energy is how much energy an object has because it is moving. It's the work done on an object to give it or keep it in motion

Assumptions

To derive an equation to describe the energy when a force gives an object motion, assume the following:

\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

$W = Δ K$ is valid for any type of energy $W = Δ E$

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