A-Level Physics: Key Formula Derivations from the June 2018 Insert Sheet | A-Level 物理：2018年6月插入表关键公式推导

📚 A-Level Physics: Key Formula Derivations from the June 2018 Insert Sheet | A-Level 物理：2018年6月插入表关键公式推导

In A-Level Physics, the insert sheet provided during exams is a valuable reference listing essential equations. The June 2018 insert (for example, AQA 7408/1) includes formulas covering mechanics, waves, fields, and electricity. While these equations are given to you, working through their derivations strengthens your conceptual understanding and equips you to tackle unfamiliar problems. This article presents clear, step-by-step derivations of key formulas from that insert, ensuring you grasp where they come from and how they connect.

在 A-Level 物理考试中，提供的插入表是列出关键方程的宝贵参考资料。2018年6月的插入表（例如 AQA 7408/1）包含了力学、波动、场和电学等公式。虽然考试中会给出这些方程，但亲手推导它们能加深你对概念的理解，并让你有能力应对陌生的问题。本文将逐步清晰地推导该插入表中的关键公式，确保你掌握它们的来源及彼此间的联系。

1. Uniform Acceleration Equations (SUVAT) | 匀加速运动方程 (SUVAT)

Under constant acceleration a, the change in velocity is uniform. By definition, acceleration is the rate of change of velocity: a = (v – u) / t. Rearranging immediately gives the first SUVAT equation: v = u + a t (Equation 1).

在匀加速度 a 下，速度的变化是均匀的。根据定义，加速度等于速度的变化率：a = (v – u) / t。整理后立刻得到第一个 SUVAT 方程：v = u + a t (方程1)。

Because acceleration is constant, the velocity–time graph is a straight line, and the average velocity is simply (u + v)/2. Displacement s equals average velocity multiplied by time: s = ((u + v)/2) t (Equation 2).

由于加速度恒定，速度-时间图是一条直线，因此平均速度就是 (u + v)/2。位移 s 等于平均速度乘以时间：s = ((u + v)/2) t (方程2)。

Substituting v from Equation 1 into Equation 2 gives s = u t + ½ a t² (Equation 3). We can also eliminate t to obtain v² = u² + 2 a s (Equation 4) and find other variants for displacement. These five equations form a complete toolkit for solving problems with constant acceleration.

将方程1中的 v 代入方程2，得到 s = u t + ½ a t² (方程3)。

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