Deriving Formulas from the AS Physics Unit 1 June 2019 Mark Scheme | 根据2019年6月AS物理单元1评分标准推导公式

📚 Deriving Formulas from the AS Physics Unit 1 June 2019 Mark Scheme | 根据2019年6月AS物理单元1评分标准推导公式

The June 2019 AS Physics Unit 1 mark scheme provides a transparent framework for what examiners expected when asking students to derive fundamental mechanics and materials equations. Understanding these derivations – and the logical steps that scores marks – is essential for high performance. This article walks through ten key formula derivations aligned with typical mark scheme requirements, pairing clear English explanations with precise Chinese translations.

2019年6月AS物理单元1的评分标准为考官期望学生推导基本力学和材料学公式提供了一个清晰的框架。理解这些推导过程以及能够得分的逻辑步骤对于取得高分至关重要。本文按照典型评分标准的要求，逐一梳理十个关键公式的推导，并配有清晰的英文解释和准确的中文翻译。

1. Deriving the SUVAT Equations | 推导匀加速运动方程

Start with the definition of constant acceleration: a = (v – u) / t, where u is initial velocity, v final velocity, and t time. Rearranging gives the first SUVAT equation v = u + a t. In the June 2019 mark scheme, this simple algebraic step is often awarded 1 mark when asked as part of a derivation question.

从恒定加速度的定义开始：a = (v – u) / t，其中 u 为初速度，v 为末速度，t 为时间。移项可得第一个运动学方程 v = u + a t。在2019年6月的评分标准中，如果推导题包含这一步，这个简单的代数操作通常可获1分。

For uniformly accelerated motion, average velocity = (u+v)/2. Displacement s equals average velocity multiplied by time: s = ((u + v)/2) × t. Substituting v = u + a t yields s = u t + ½ a t². Mark schemes reward explicit substitution and expansion.

对于匀加速运动，平均速度 = (u+v)/2。位移 s 等于平均速度乘以时间：s = ((u + v)/2) × t。代入 v = u + a t 得到 s = u t + ½ a t²。评分标准对清晰的代入和展开给予分数。

To obtain the time-independent relation, express t = (v – u)/a from the first equation and substitute into s = ((u+v)/2) × t. After simplification, you obtain v² = u² + 2 a s. Examiners often expect candidates to show the elimination of t fully.

要得到不含时间的公式，可从第一式表达 t = (v – u)/a，代入 s = ((u+v)/2) × t。化简后得到 v² = u² + 2 a s。考官通常期望考生完整展示消去 t 的过程。

2. Deriving Kinetic Energy E_k = ½ m v² | 推导动能公式 E_k = ½ m v²

Consider a constant net force F acting on a mass m from rest, causing acceleration a. The work done W = F s. Using Newton’s second law, F = m a, and the kinematic relation v² = 2 a s (with u=0), solve for acceleration: a = v²/(2s). The mark scheme expects you to connect force, displacement and velocity clearly.

考虑恒定的合外力 F

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