A-Level Physics Insert 4 Jan22: Deriving Key Formulae | A-Level物理 Insert 4 Jan22 公式推导

📚 A-Level Physics Insert 4 Jan22: Deriving Key Formulae | A-Level物理 Insert 4 Jan22 公式推导

The A-Level Physics Insert for January 2022 (Paper 4) is a datasheet of essential formulae provided during the exam. While you can use these equations directly, understanding their derivations deepens your grasp of physical principles and improves problem-solving skills. This article explores the step-by-step derivations of some of the most critical formulae from the insert.

A-Level 物理 2022 年 1 月考试（Paper 4）提供的公式表是一份包含核心方程的数据插页。虽然你可以直接使用这些公式，但理解它们的推导过程能加深你对物理原理的掌握，并提高解题能力。本文将逐步推导该公式表中一些最关键公式的来源。

1. Kinematic Equations (SUVAT) | 运动学公式（SUVAT）

Consider an object moving with constant acceleration a from initial velocity u to final velocity v over time t. Acceleration is defined as the rate of change of velocity:

考虑一个物体以恒定加速度 a 从初速度 u 加速到末速度 v，历时 t。加速度定义为速度的变化率：

a = (v − u) / t ⟹ v = u + a t

This gives the first SUVAT equation. For displacement s, we use the average velocity, which is (u+v)/2 for constant acceleration. Since displacement is average velocity multiplied by time:

由此得出第一个 SUVAT 方程。对于位移 s，我们使用平均速度，恒加速下为 (u+v)/2。因为位移等于平均速度乘以时间：

s = ((u + v)/2) t

Substitute v = u + a t into the displacement equation:

将 v = u + a t 代入位移方程：

s = u t + ½ a t²

To eliminate time, solve v = u + a t for t and substitute into s = ((u+v)/2) t:

为了消去时间，从 v = u + a tPublished by TutorHao | A-Level Physics Revision Series | aleveler.com

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