Pre-U AQA PE: Formula & Theorem Quick Reference Guide | Pre-U AQA 体育：公式定理速查手册

📚 Pre-U AQA PE: Formula & Theorem Quick Reference Guide | Pre-U AQA 体育：公式定理速查手册

This handbook provides a concise, exam-focused summary of the essential formulas and scientific theorems from the Pre-U AQA Physical Education specification. Covering biomechanics, exercise physiology, skill acquisition and training principles, these equations underpin performance analysis, data interpretation and theoretical understanding in sport and exercise science. Use this guide alongside past papers and practical examples to master quantitative PE skills.

本手册依据 Pre-U AQA 体育课程要求，精炼梳理了核心公式与科学定理。涵盖运动生物力学、运动生理学、技能习得与训练原则，这些方程是运动表现分析、数据解读与运动科学理论理解的基础。请结合历年真题与实践案例使用，扎实掌握定量分析能力。

1. Linear Motion (SUVAT) Equations | 线性运动方程

The SUVAT equations describe uniformly accelerated motion along a straight line. The variables are displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). Always define a positive direction and apply a consistent sign convention when velocities or accelerations act in opposite directions.

SUVAT 方程描述沿直线的匀加速运动。变量包括位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）。当速度或加速度方向相反时，必须定义正方向并统一正负号规则。

v = u + at  — relates velocity to acceleration and time, with no displacement term.

v = u + at — 关联速度、加速度和时间，不含位移项。

s = ut + ½ a t²  — calculates displacement when final velocity is unknown.

s = ut + ½ a t² — 末速度未知时用于计算位移。

v² = u² + 2as  — links velocities, acceleration and displacement without involving time.

v² = u² + 2as — 连接速度、加速度和位移，不涉及时间变量。

s = ½ (u + v) t  — uses average velocity, valid only when acceleration is constant.

s = ½ (u + v) t — 利用平均速度，仅在加速度恒定时有效。

In free fall where only gravity acts, set a = g = 9.81 m s⁻² and use vertical motion components; upward velocities are usually taken as positive.

在仅受重力作用的自由落体中，设 a = g = 9.81 m s⁻² 并采用竖直运动分量；通常取向上速度为正。

2. Projectile Motion | 抛体运动

Projectile motion can be resolved into independent horizontal and vertical components. The horizontal velocity remains constant when air resistance is negligible, while vertical motion is subject to uniform acceleration due to gravity (g = 9.81 m s⁻²). The launch velocity v is split into uₓ = v cos θ and uy = v sin θ, where θ is the angle of release.

抛体运动可分解为独立的水平与竖直分量。忽略空气阻力时水平速度恒定，竖直方向受匀重力加速度（g = 9.81 m s⁻²）作用。发射速度 v 分解为 uₓ = v cos θ 和 uy = v sin θ，θ 为出手角度。

Horizontal displacement: x = uₓ t  — no acceleration in horizontal direction.

水平位移：x = uₓ t — 水平方向无加速度。

Vertical displacement: y = uy t – ½ g t²  — upward initial velocity slows down due to gravity.

竖直位移：y = uy t – ½ g t² — 向上的初速度因重力而渐减。

Vertical velocity at any time: vy = uy – g t  — negative when the object is falling.

任意时刻竖直速度：vy = uy – g t — 物体下落时该值为负。

Time of flight for symmetrical trajectory (same launch and landing height): T = 2 uy / g.

对称轨迹的总飞行时间（起落点同高）：T = 2 uy / g。

Maximum height: H = uy² / (2g)  — reached when vy = 0.

最大高度：H = uy² / (2g) — 在 vy = 0 时达到。

3. Newton’s Laws, Momentum and Impulse | 牛顿定律、动量与冲量

Newton’s First Law: an object remains at rest or in uniform motion unless acted upon by an external resultant force.

牛顿第一定律：若物体不受外合力作用，则保持静止或匀速直线运动状态。

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