📚 IGCSE Edexcel Physics: Kinetics Key Points | IGCSE Edexcel 物理：动力学 考点精讲
In the Edexcel IGCSE Physics specification (4PH1), the topic that students casually call "kinetics" is really kinematics - the language used to describe how things move. It sits at the very start of Section 1, Forces and Motion, and it underpins almost every later topic, from Newton's laws to momentum and energy. This guide walks through every key point examiners test: the definitions of distance, displacement, speed, velocity and acceleration; how to read and draw motion graphs; how to select and apply the equations of motion; how free fall and terminal velocity behave; and how to avoid the mistakes that cost marks in Paper 1 and Paper 2.
在 Edexcel IGCSE 物理考纲（4PH1）中，学生口中常说的"动力学"，严格来说是"运动学"（kinematics）——即用来描述物体如何运动的语言体系。它位于第一部分"力与运动"的最开头，是后面牛顿定律、动量与能量等几乎所有章节的基础。本文系统梳理考官真正会考的全部要点：距离、位移、速率、速度与加速度的定义；运动图像的读取与绘制；运动学公式的选用与代入；自由落体与终端速度的行为；以及 Paper 1 和 Paper 2 中最容易丢分的常见错误。
1. What "Kinetics" Covers in Edexcel IGCSE Physics | 一、Edexcel IGCSE 物理中"动力学"的考查范围
In exam papers the topic is never labelled "kinetics". The command words you will meet are describe the motion of, calculate the speed of, state the acceleration of and explain why the velocity changes. Everything in this topic is examined through three routes: a written description, a numerical calculation, and a graph. If you can move confidently between those three representations of the same motion, you have mastered the topic.
在真题中，这个知识点从来不会直接标成"kinetics"。你真正会遇到的指令词是：describe the motion of（描述……的运动）、calculate the speed of（计算……的速率）、state the acceleration of（写出……的加速度）、explain why the velocity changes（解释速度为何改变）。本考点通过三条路径被考查：文字描述、数值计算、图像。如果你能在同一段运动的这三种表达之间自由切换，这个考点就真正掌握了。
The specification places kinematics inside Section 1 alongside forces, moments, momentum and energy. Examiners therefore rarely test it in isolation. A typical question gives you a velocity-time graph for a car and then asks for the resultant force, the kinetic energy, or the braking distance. The kinematics is only step one, but if step one is wrong, every later mark disappears.
考纲把运动学放在第一部分，与力、力矩、动量、能量并列。因此考官很少单独考查它。典型题目会给你一张汽车的"速度-时间"图像，然后追问合力、动能或刹车距离。运动学只是第一步，但第一步算错，后面所有分都会连带丢失。
- Recall marks: state the equation linking speed, distance and time; give the unit of acceleration. | 记忆分：写出连接速率、距离、时间的公式；给出加速度的单位。
- Application marks: substitute into v = u + at or v² = u² + 2as and obtain a correctly rounded answer. | 应用分：代入 v = u + at 或 v² = u² + 2as，得出正确取整的结果。
- Analysis marks: interpret the gradient or the area under a graph, including curved sections. | 分析分：解读图像的斜率或面积，包括曲线部分。
- Practical marks: describe how to measure speed or acceleration using light gates or a stopwatch, and identify the main source of uncertainty. | 实验分：描述如何用光电门或秒表测量速率或加速度，并指出主要误差来源。
2. Scalars and Vectors: Distance, Displacement, Speed, Velocity | 二、标量与矢量：距离、位移、速率、速度
A scalar quantity has magnitude only. A vector quantity has both magnitude and direction. This distinction is not decoration - it is the reason distance and displacement can have different values for the same journey, and it is frequently worth a mark on its own.
标量只有大小，矢量既有大小又有方向。这个区分不是装饰——它正是"同一段路程中距离与位移可以不同"的根本原因，本身也经常单独占一分。
Distance is the total length of the path travelled, measured in metres. It is a scalar. Displacement is the straight-line distance from start to finish, together with the direction, also in metres, but a vector. If a runner completes one lap of a 400 m track and stops at the start line, the distance is 400 m but the displacement is 0 m.
距离是实际经过路径的总长度，单位是米，属于标量。位移是从起点到终点的直线距离，并附带方向，单位同样是米，但属于矢量。若运动员绕 400 m 跑道跑完一圈回到起点，则距离为 400 m，而位移为 0 m。
Speed ow fast something moves, regardless of direction: speed = distance ÷ time. It is a scalar. Velocity is speed in a stated direction, a vector. A car travelling at 20 m/s north and a car travelling at 20 m/s south have the same speed but opposite velocities.
速率表示运动的快慢，与方向无关：速率 = 距离 ÷ 时间，是标量。速度是"带方向的速率"，是矢量。一辆车以 20 m/s 向北行驶，另一辆以 20 m/s 向南行驶，两者速率相同，速度方向相反。
| Scalar 标量 | Vector 矢量 |
| distance 距离 | displacement 位移 |
| speed 速率 | velocity 速度 |
| mass 质量, time 时间, energy 能量 | acceleration 加速度, force 力, momentum 动量, weight 重力 |
An object moving in a circle at a constant speed is still accelerating, because its direction - and therefore its velocity - keeps changing. This single idea explains a great deal of circular motion later in the course.
物体做匀速圆周运动时速率不变，但仍然在加速，因为它的方向不断改变，速度因而不断改变。这一个观念解释了课程后面大量圆周运动的问题。
3. Calculating Speed and Average Speed | 三、速率与平均速率的计算
The basic relationship is the most examined equation in the whole topic. Learn it in all three rearranged forms so that you never lose time in the exam.
这个基本关系式是整个考点中被考查次数最多的公式。请把三种变形都背熟，考场上就不会浪费时间。
v = s ÷ t s = v × t t = s ÷ v
Here v is speed in metres per second (m/s), s is distance in metres (m) and t is time in seconds (s). If a question supplies kilometres or minutes, convert before substituting - this is the single most common source of lost marks in calculation questions.
其中 v 是速率，单位米每秒（m/s）；s 是距离，单位米（m）；t 是时间，单位秒（s）。若题目给出千米或分钟，必须先换算再代入——这是计算题中最常见的失分点。
Average speed is the total distance divided by the total time, and it is not the same as the mean of two speeds unless the two stages took equal times. Instantaneous speed is the speed at one particular moment, found from the gradient of a distance-time graph or read directly from a speedometer.
平均速率等于总距离除以总时间；除非两个阶段所用时间相等，否则它并不等于两个速率的算术平均值。瞬时速率是某一瞬间的速率，可由"距离-时间"图像在该点的斜率求出，或直接从车速表上读出。
1 km/h = 1 ÷ 3.6 m/s ≈ 0.28 m/s 1 m/s = 3.6 km/h
| Situation 情景 | Typical speed 典型速率 |
| walking 步行 | 1.5 m/s |
| running 跑步 | 3 m/s |
| cycling 骑车 | 6 m/s |
| car on a motorway 高速公路汽车 | 25 to 30 m/s |
| sound in air 空气中的声 | 330 m/s |
| light in a vacuum 真空中的光 | 3.0 × 10⁸ m/s |
first: 1.8 km = 1800 m and 3 min = 180 s. Then v = 1800 ÷ 180 = 10 m/s, which is 36 km/h.
例题：一名骑车人 3 分钟骑行 1.8 km。先换算：1.8 km = 1800 m，3 min = 180 s。于是 v = 1800 ÷ 180 = 10 m/s，即 36 km/h。
4. Acceleration: Definition, Unit and Sign | 四、加速度：定义、单位与符号
Acceleration is the rate of change of velocity. Because velocity is a vector, an object accelerates if it speeds up, if it slows down, or if it changes direction while travelling at a constant speed.
加速度是速度的变化率。由于速度是矢量，物体加速的情形包括：变快、变慢，以及速率不变但方向改变。
a = (v − u) ÷ t
Here u is the initial velocity, v is the final velocity, both in m/s, and t is the time taken in seconds. The unit of acceleration is metres per second squared (m/s²), which means "metres per second of velocity change, every second".
其中 u 是初速度，v 是末速度，单位都是 m/s；t 是所用时间，单位秒。加速度的单位是米每二次方秒（m/s²），含义是"每秒钟速度改变多少米每秒"。
If v is smaller than u, the answer is negative. A negative acceleration is called a deceleration, and both a negative sign and the word deceleration are accepted by examiners, provided the working shows you understand the direction.
若 v 小于 u，结果就是负值。负加速度称为减速度；只要解题过程体现出你对方向的理解，写负号或写 deceleration 考官都认可。
12 m/s in 8.0 s. Then a = (12 − 40) ÷ 8.0 = −3.5 m/s². The train decelerates at 3.5 m/s².
例题：列车在 8.0 s 内由 40 m/s 减速到 12 m/s。则 a = (12 − 40) ÷ 8.0 = −3.5 m/s²，即列车以 3.5 m/s² 减速。
- Acceleration is not the same as speed. A car cruising at 30 m/s has zero acceleration. | 加速度不等于速率。以 30 m/s 匀速巡航的汽车加速度为零。
- Zero acceleration means constant velocity, not zero velocity. | 加速度为零意味着速度不变，而不是速度为零。
- An object at rest can still have acceleration - for example a ball at the top of its flight. | 静止的物体也可以有加速度——例如上抛到最高点的小球。
5. Distance-Time Graphs | 五、距离-时间图像
s the speed at that point, because gradient = change in y ÷ change in x = distance ÷ time.
"距离-时间"图像以竖直轴表示已走过的距离，水平轴表示时间。图线上任意一点的斜率就等于该点的速率，因为斜率 = y 的变化量 ÷ x 的变化量 = 距离 ÷ 时间。
| Shape of line 线段形状 | Meaning 含义 |
| horizontal 水平 | stationary, speed 0 m/s 静止，速率为零 |
| straight line with constant gradient 恒定斜率的直线 | constant speed 匀速运动 |
| steeper straight line 更陡的直线 | higher speed 速率更大 |
| curve getting steeper 越来越陡的曲线 | accelerating 加速 |
| curve flattening 逐渐变平的曲线 | decelerating 减速 |
| line sloping down 向下的斜线 | returning towards the start 返回起点方向 |
When the graph is curved, the speed at a given instant is found by drawing a tangent at that point and calculating the tangent's gradient. Choose two points on the tangent that are as far apart as possible, and read the axes carefully - the tangent line must touch the curve at the point of interest and nowhere else.
若图像是曲线，求某一瞬间的速率的方法是：在该点作切线，再计算切线的斜率。切线上的两点要尽量取远一些，读数要仔细——切线只在所求点与曲线相切，其余位置不相交。
6.0) ÷ (6.0 − 2.0) = 12.0 ÷ 4.0 = 3.0 m/s, so the instantaneous speed at 4.0 s is 3.0 m/s.
例题：在 t = 4.0 s 处所作切线经过点 (2.0 s, 6.0 m) 与 (6.0 s, 18.0 m)，斜率为 (18.0 − 6.0) ÷ (6.0 − 2.0) = 12.0 ÷ 4.0 = 3.0 m/s，故 4.0 s 时的瞬时速率为 3.0 m/s。
Note the trap: a distance-time graph never shows a vertical line for an instantaneous stop, and the height of the line tells you nothing about the speed on its own - only the gradient does.
注意陷阱："距离-时间"图像中不会出现表示"瞬间停下"的竖直线；而且图线的高度本身与速率无关，只有斜率才反映速率。
6. Velocity-Time Graphs | 六、速度-时间图像
In a velocity-time graph, velocity is plotted on the vertical axis. Now the gradient gives acceleration and the area between the line and the time axis gives the distance travelled. These two rules are the most heavily examined ideas in the whole topic.
在"速度-时间"图像中，竖直轴表示速度。此时斜率给出加速度，而图线与时间轴之间的面积给出走过的距离。这两条规则是整个考点中考查频率最高的内容。
ient = acceleration = (v − u) ÷ t area under graph = distance travelled
| Shape of line 线段形状 | Meaning 含义 |
| on the time axis 与时间轴重合 | at rest 静止 |
| horizontal above the axis 轴上方水平线 | constant velocity 匀速运动 |
| straight line sloping up 向上斜直线 | uniform acceleration 匀加速 |
| straight line sloping down to the axis 向下斜至时间轴 | uniform deceleration to rest 匀减速至停止 |
| line crossing below the axis 穿过时间轴下方 | motion in the opposite direction 反向运动 |
llel sides) × height. For a curve, count squares under the graph, estimating part squares.
求面积时，把图形分割为矩形与三角形，或直接按梯形公式 面积 = ½ ×（上底 + 下底）× 高 计算。若图线是曲线，则数图线下的方格数，不满一格的部分进行估算。
tion phase has a = (24 − 0) ÷ 6.0 = 4.0 m/s². Total distance = ½ × 6.0 × 24 + 10 × 24 + ½ × 4.0 × 24 = 72 + 240 + 48 = 360 m.
例题：汽车由静止匀加速 6.0 s 达到 24 m/s，随后以 24 m/s 匀速行驶 10 s，再匀减速 4.0 s 停下。加速阶段 a = (24 − 0) ÷ 6.0 = 4.0 m/s²；总距离 = ½ × 6.0 × 24 + 10 × 24 + ½ × 4.0 × 24 = 72 + 240 + 48 = 360 m。
Always check the units on both axes before you start, and state clearly which quantity you are calculating. A common error is to give the gradient when the question asked for the area, or the other way round.
动笔前先确认两轴的单位，并明确写出你正在求的是什么量。最常见的错误是：题目要面积，你给了斜率；或者反过来。
7. The Equations of Motion (SUVAT) | 七、运动学公式（SUVAT）
When motion involves uniform acceleration, the graph method becomes slow. Four equations link the five quantities s, u, v, a and t. Each equation is missing exactly one of these quantities, and that is precisely how you choose between them.
当运动是匀加速时，用图像法太慢。四个公式把 s、u、v、a、t 五个量联系起来。每个公式恰好缺少其中一个量，这正是选择公式的依据。
v = u + at (missing s)
s = ((u + v) ÷ 2) × t (missing a)
s = ut + ½at² (missing v)
v² = u² + 2as (missing t)
Here s is displacement in metres, u and v are initial and final velocity in m/s, a is acceleration in m/s² and t is time in seconds. The equations only work if the acceleration is constant, so never use them across a graph where the gradient changes.
其中 s 是位移（m），u 与 v 是初、末速度（m/s），a 是加速度（m/s²），t 是时间（s）。这些公式只在加速度恒定时成立，因此不能跨越图像中斜率发生变化的区段使用。
- Write down u, v, a, s and t, fill in what you know, then choose the equation with exactly one unknown. | 先列出 u、v、a、s、t 五个量，填入已知值，再选择只有一个未知量的公式。
- Choose a positive direction at the start and keep it. If up is positive, then g is negative. | 一开始就规定正方向并坚持到底。若取向上为正，则 g 取负值。
- Never mix metres with centimetres or seconds with minutes. | 绝不要把米与厘米、秒与分钟混用。
- Give the answer to the same number of significant figures as the least precise data, usually 2 or 3. | 答案的有效数字应与最不精确的数据一致，通常为 2 或 3 位。
ked example: a car accelerates uniformly from 8.0 m/s to 26 m/s over 120 m. Which equation? = u² + 2as. Rearranging: a = (v² − u²) ÷ (2s) = (676 − 64) ÷ 240 = 612 ÷ 240 = 2.55 m/s².
例题：汽车由 8.0 m/s 匀加速到 26 m/s，位移 120 m。已知 u、v、s，求 a，故选 v² = u² + 2as。变形得 a = (v² − u²) ÷ (2s) = (676 − 64) ÷ 240 = 612 ÷ 240 = 2.55 m/s²。
8. Free Fall and the Acceleration Due to Gravity | 八、自由落体与重力加速度
Near the Earth' en the symbol g, and Edexcel questions normally supply g = 9.8 m/s² or g = 10 m/s² in the rubric, so always use the value printed on the paper.
在地表附近，任何*自由*下落（即空气阻力可忽略）的物体都以约 9.8 m/s² 向下加速。该值记作 g；Edexcel 题目通常在卷首给出 g = 9.8 m/s² 或 g = 10 m/s²，务必使用试卷上给出的数值。
Because g is the same for all objects, a heavy ball and a light ball released together from the same height land at the same time in a vacuum. In air, the difference comes entirely from air resistance, not from weight.
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