Kinetic & Potential Energy (Edexcel A-Level Further Mathematics): Revision Notes

14.1.1 Kinetic & Potential Energy

Introduction

Kinetic and potential energy are two key forms of mechanical energy. These concepts are fundamental to understanding motion and energy transformations. In this note, we focus on:

1. Kinetic Energy (KE): The energy of motion.
2. Potential Energy (PE): The energy due to position relative to a reference level. We will use these ideas to solve problems involving motion under gravity, often on an inclined plane.

Kinetic Energy (KE)

The kinetic energy of an object of mass $m$ moving with velocity $v$ is given by:

$$KE = \frac{1}{2}mv^2$$

where:

• $m$ is the mass ($\text{kg}$)
• $v$ is the velocity ($\text{ms}^{-1}$) Kinetic energy is always non-negative and depends on the square of the speed.

Potential Energy (PE)

The potential energy of an object of mass $m$ at height $h$ above a reference point is:

$$PE = mgh$$

where:

• $g$ is the acceleration due to gravity ($:highlight[9.8] \, \text{ms}^{-2}$)
• $h$ is the height ($\text{m}$) Potential energy depends on the relative position of the object.

Worked Examples

Note Summary