📚 A-Level CAIE Physical Education: Formula & Theorem Quick Reference Handbook | A-Level CAIE 体育：公式定理速查手册
This handbook summarises the key formulae, laws and quantitative relationships that appear in the CAIE A Level Physical Education (9396) syllabus. It is designed as a fast reference for biomechanics, exercise physiology and skill acquisition questions. Each entry includes the formula, SI units and a practical sporting example.
本手册总结了 CAIE A Level 体育（9396）大纲中出现的核心公式、定律和数量关系，可作为生物力学、运动生理学和技能学习相关题目的快速参考。每项都列出公式、国际单位和一个运动实例。
1. Linear Kinematics | 线运动学基础
In linear motion, average velocity is the displacement divided by the time taken. Displacement is a vector, so direction matters; distance is a scalar and ignores direction.
在线运动中，平均速度等于位移除以所用时间。位移是矢量，因此方向很重要；路程是标量，不考虑方向。
v = s ÷ t
Acceleration is the change in velocity per unit time. It is positive when speeding up in the chosen direction and negative when slowing down.
加速度是单位时间内速度的变化量。沿选定方向加速时为正，减速时为负。
a = (v - u) ÷ t
For uniform acceleration, three equations link initial velocity u, final velocity v, acceleration a, displacement s and time t. These are used to analyse sprint starts, long jump take-offs and projectile-like motions when air resistance is ignored.
对于匀加速运动，三个方程将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系起来。它们用于分析短跑起跑、跳远起跳以及忽略空气阻力时的类抛体运动。
v = u + at
s = ut + ½at²
v² = u² + 2as
All units are SI: metres (m), seconds (s), metres per second (m s⁻¹), metres per second squared (m s⁻²).
所有单位均为国际单位：米（m）、秒（s）、米每秒（m s⁻¹）、米每二次方秒（m s⁻²）。
2. Newton's Laws and Momentum | 牛顿定律与动量
Newton' of change of its momentum. For constant mass, this reduces to force = mass × acceleration.
牛顿第二定律指出，作用在物体上的合力等于其动量变化率。质量不变时，可简化为力 = 质量 × 加速度。
F = ma
Momentum p is the product of mass and velocity, measured in kg m s⁻¹. A heavier or faster athlete has greater momentum and is harder to stop or change direction.
动量 p 是质量与速度的乘积，单位为 kg m s⁻¹。体重更大或速度更快的运动员动量更大，更难被停止或改变方向。
p = mv
Impulse equals the applied force multiplied by contact time, and it equals the change in momentum. This explains why follow-through in a tennis stroke increases impulse and ball speed, and why bending the knees on landing increases impact time to reduce force.
冲量等于作用力乘以接触时间，也等于动量的变化量。这解释了为什么网球挥拍的随挥动作能增大冲量和球速，以及为什么落地屈膝能延长冲击时间从而减小作用力。
Impulse = Ft = Δp
3. Work, Energy and Power | 功、能量与功率
Work is done when a force moves its point of application. In sport, muscular work transfers chemical energy into mechanical energy.
当力的作用点发生位移时就做了功。在运动中，肌肉做功将化学能转化为机械能。
W = Fd
Kinetic energy is the energy of motion, and gravitational potential energy is stored due to height above a reference level. Both are measured in joules (J).
动能是运动具有的能量，重力势能是因高于参考水平面而储存的能量。两者单位均为焦耳（J）。
