📚 Year 9 WJEC PE: Formula & Theorem Quick Reference Handbook | WJEC 9年级体育：公式定理速查手册
This handbook brings together the essential formulas, theorems and key physiological calculations required for the Year 9 WJEC Physical Education course. It covers biomechanics principles, body composition indices, heart rate training zones, lever mechanics and perceived exertion scales. Each entry is presented with a clear formula, a worked example where appropriate, and paired bilingual explanations to support revision and quick recall.
本手册汇集了 WJEC 9年级体育课程所需的基本公式、定理和关键生理学计算。内容涵盖生物力学原理、体成分指数、心率训练区间、杠杆力学和主观用力感觉量表。每个条目均给出清晰公式，必要时附示例计算，并配有中英双语解释，以辅助复习和快速记忆。
1. Speed, Distance and Time | 速度、距离与时间
Speed is a scalar quantity defined as the distance travelled per unit of time. It is one of the most fundamental measurements in sports biomechanics, used to analyse running, cycling, swimming and ball movement.
速度是标量，定义为单位时间内通过的距离。它是运动生物力学中最基本的测量指标之一，用于分析跑步、骑行、游泳和球的运动。
Speed = Distance ÷ Time
12.5 seconds, the average speed is 100 ÷ 12.5 = 8 m/s. WJEC questions often require converting units, e.g. metres per second to kilometres per hour (multiply by 3.6), or calculating split times.
变换此关系式可得，距离等于速度乘以时间，时间等于距离除以速度。在一项 12.5 秒完成的 100 米短跑中，平均速度为 100 ÷ 12.5 = 8 米/秒。WJEC 考题常要求换算单位，例如将米/秒换算为公里/小时（乘以3.6），或计算分段用时。
2. Acceleration | 加速度
Acceleration describes how quickly velocity changes. It is a vector quantity, meaning it has both magnitude and direction. In sport, athletes accelerate from a stationary start, decelerate when braking, and change direction rapidly.
加速度描述速度变化的快慢。它是一个矢量，既有大小又有方向。在运动中，运动员从静止开始加速，制动时减速，并快速改变方向。
Acceleration (a) = (Final Velocity − Initial Velocity) ÷ Time taken
a = (v − u) ÷ t
tive acceleration, or deceleration, occurs when final velocity is less than initial velocity. Understanding acceleration helps coaches design drills that improve an athlete's ability to reach top speed quickly.
若一名足球运动员在2秒内速度由0 m/s增至7 m/s，加速度为 (7 − 0) ÷ 2 = 3.5 m/s²。当末速度小于初速度时，出现负加速度（减速）。理解加速度有助于教练设计训练以提升运动员快速达到最高速度的能力。
3. Force and Newton's Laws of Motion | 力与牛顿运动定律
Force is any interaction that, when unopposed, changes the motion of an object. Newton's three laws form the foundation of linear mechanics and are directly applied to sports performance.
力是任何能够改变物体运动状态的相互作用。牛顿三定律构成了线性力学的基础，并可直接应用于运动表现。
Force (F) = Mass (m) × Acceleration (a)
First Law (Law of Inertia): An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. A football will not move until kicked.
第一定律（惯性定律）： 除非受外力作用，物体将保持静止或匀速直线运动状态。足球不被踢就不会移动。
Second Law (F = ma): The acceleration of an object is proportional to the net force and inversely proportional to its mass. A lighter shot put can be thrown further with the same force.
第二定律 (F = ma)： 物体的加速度与所受净力成正比，与质量成反比。用同样的力，较轻的铅球能被投得更远。
Third Law (Action–Reaction): For every action there is an equal and opposite reaction. When a swimmer pushes water backwards, the water pushes the swimmer forwards.
第三定律（作用与反作用）： 每一个作用力都有一个大小相等、方向相反的反作用力。游泳者向后推水时，水将游泳者向前推。
4. Momentum and Impulse | 动量与冲量
Momentum quantifies how difficult it is to stop a moving object. It is the product of mass and velocity. Impulse measures the effect of a force acting over a time interval, and equals the change in momentum.
动量用来衡量使运动物体停止的难易程度。它是质量与速度的乘积。冲量衡量在一段时间内力的作用效果，并等于动量的变化量。
Momentum (p) = Mass (m) × Velocity (v)
Impulse = Force (F) × Time (t) = Δp
In contact sports, increasing the time over which a force is applied reduces the instantaneous impact. For example, a cricketer moving their hands backward when catching a ball increases the impulse time, reducing the sting. Similarly, a long follow-through in a golf swing extends gain in momentum.
在身体接触运动中，延长力的作用时间可降低瞬时冲击。例如，板球运动员接球时双手后撤可延长冲量作用时间，减小刺痛感。同样地，高尔夫挥杆中充分的随挥动作可延长动量的增长。
5. Maximum Heart Rate and Training Zones | 最大心率与训练区间
Maximum Heart Rate (HRmax) is the highest number of beats per minute your heart can achieve during maximal exercise. A simple estimation is commonly used for setting training intensities.
最大心率 (HRmax) 是你在极量运动中心脏能达到的每分钟最高搏动次数。一个简单的估算公式通常用于设定训练强度。
HRmax = 220 − Age
Using %HRmax, five training zones can be defined:
利用最大心率百分比，可界定五个训练区间：
| Zone 区间 | % HRmax | Physiological Benefit 生理收益 |
|---|---|---|
| Recovery | 50–60% | Active recovery, warm-up / 主动恢复，热身 |
| Aerobic (Fat-burning) | 60–70% | Improves endurance and fat metabolism / 提高耐力与脂肪代谢 |
| Aerobic/Anaerobic (Threshold) | 70–80% | Raises lactate threshold, cardiovascular capacity / 提升乳酸阈，心血管功能 |
| Anaerobic | 80–90% | Develops speed and high-intensity tolerance / 发展速度和高强度耐受力 |
| Maximum Effort | 90–100% | Peak power, neuromuscular coordination / 最大功率，神经肌肉协调 |
WJEC PE tasks often require you to calculate a target heart rate range for a given athlete using these percentages.
WJEC 体育考试常要求你使用这些百分比为指定运动员计算目标心率区间。
6. Karvonen Formula (Heart Rate Reserve) | 卡氏公式（心率储备）
The Karvonen formula uses resting heart rate (HRrest) to create a more individualised training intensity. It calculates the heart rate reserve (HRR) and adds a percentage of this reserve back to the resting value.
卡氏公式利用安静心率 (HRrest) 制定更个性化的训练强度。它计算心率储备 (HRR)，并将该储备的一定百分比加回到安静心率值上。
Heart Rate Reserve (HRR) = HRmax − HRrest
Target Heart Rate = (HRR × %Intensity) + HRrest
Worked example: a 14-year-old athlete with HRrest = 62 bpm wants to train at 75% fitness level because a fitter person typically has a lower HRrest, widening the reserve.
示例计算：一名14岁运动员安静心率62次/分，希望以75%强度训练。最大心率=220−14=206 bpm。心率储备=206−62=144 bpm。目标心率=(144×0.75)+62=170 bpm。此方法可根据体能水平进行调整，因为更健康的人通常安静心率较低，从而使储备范围增大。
7. Body Mass Index (BMI) | 身体质量指数
BMI is a widely used screening tool that relates body weight to height. Although it does not directly measure body fat, it provides a quick indication of whether a person is underweight, healthy, overweight or obese.
BMI 是一种广泛使用的筛查工具，将体重与身高联系起来。尽管它不能直接测量体脂，但可快速指示一个人是否过轻、健康、超重或肥胖。
BMI = Weight (kg) ÷ Height² (m)
the square of height in metres. For a student weighing 55 kg and 1.65 m tall: BMI = 55 ÷ (
Published by TutorHao | Year 9 体育 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图