IGCSE CIE Physics: Kinematics Revision | IGCSE CIE 物理：动力学考点精讲

📚 IGCSE CIE Physics: Kinematics Revision | IGCSE CIE 物理：动力学考点精讲

Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. For IGCSE CIE Physics, you need to understand key concepts such as distance, displacement, speed, velocity and acceleration, and you must be able to interpret motion graphs and apply the equations of uniformly accelerated motion. This revision guide breaks down each of these topics into clear, bite-sized sections, with paired explanations in English and Chinese to support bilingual learners. By the end, you will have a thorough grasp of the core ideas and be well prepared for both the multiple-choice questions and the structured theory paper.

动力学是物理学的分支，描述物体的运动而不考虑引起运动的力。对于 IGCSE CIE 物理，你需要理解距离、位移、速率、速度和加速度等核心概念，还必须能够解读运动图像并应用匀加速运动方程。这份考点精讲将每个主题分解为清晰的小节，配以中英文对照的解释，帮助双语学习者掌握重点。学完这些内容后，你将透彻理解核心思想，为选择题和结构化理论考试做好充分准备。

1. Scalar and Vector Quantities | 标量与矢量

In physics, quantities are divided into scalars and vectors. A scalar quantity has magnitude (size) only. Examples include distance, speed, mass and time. A vector quantity has both magnitude and direction. Velocity, displacement, force and acceleration are vectors. Understanding this distinction is vital because vector quantities cannot be added or subtracted in the same simple way as scalars; direction must be taken into account.

在物理学中，物理量分为标量和矢量。标量只有大小，例如距离、速率、质量和时间。矢量既有大小又有方向，速度、位移、力和加速度都是矢量。理解这一区别至关重要，因为矢量的加减运算不能像标量那样简单，必须考虑方向。

When you represent a vector on a diagram, you draw an arrow whose length indicates the magnitude and whose orientation shows the direction. In kinematics problems, the sign of a vector (positive or negative) is used to indicate its direction along a straight line. For example, if you choose the right as positive, a velocity of +5 m/s means moving to the right, while -5 m/s means moving to the left.

在图上表示矢量时，箭头长度表示大小，箭头方向表示方向。在运动学问题中，矢量的正负号用于表示沿直线的方向。例如，如果规定向右为正，那么速度 +5 m/s 表示向右运动，-5 m/s 表示向左运动。

2. Distance and Displacement | 距离与位移

Distance is a scalar quantity that measures the total length of the path travelled by an object. Displacement is a vector that describes the straight-line distance from the starting point to the final position, together with its direction. If you walk around a 400 m running track and return to your starting point, your distance travelled is 400 m, but your displacement is 0 m because there has been no overall change in position.

距离是标量，测量物体运动轨迹的总长度。位移是矢量，描述从起点到终点的直线距离及其方向。如果你绕 400 米跑道走一圈回到起点，走过的距离是 400 米，但位移为 0 米，因为位置没有发生净变化。

In IGCSE exams, you may be asked to draw a scale diagram to find the resultant displacement when an object moves in two perpendicular directions. Using Pythagoras’ theorem or a carefully measured vector triangle is the correct approach. Always remember to include both the magnitude and the direction in your final answer for displacement.

在 IGCSE 考试中，你可能会被要求按比例画图，求物体沿两个垂直方向运动时的合位移。正确方法是使用勾股定理或小心测量矢量三角形。记住，最终表示位移的答案必须包含大小和方向。

3. Speed and Velocity | 速率与速度

Speed is the rate at which an object covers distance. It is a scalar and is calculated as distance travelled divided by time taken. The formula is speed = distance / time, or in symbols: s = d / t. Velocity, on the other hand, is the rate of change of displacement. It is a vector and is given by velocity = displacement / time. If an object moves in a straight line without changing direction, its speed and the magnitude of its velocity are the same.

速率是物体通过距离的快慢程度，它是一个标量，计算公式为：速率 = 距离 / 时间，即 s = d / t。而速度是位移的变化率，它是一个矢量，公式为：速度 = 位移 / 时间。如果物体沿直线运动且方向不变，其速率和速度的大小是相同的。

Average speed is the total distance travelled divided by the total time taken, while instantaneous speed is the speed at a specific moment. When a car’s speedometer shows 60 km/h, that is the instantaneous speed. In graph work, the slope (gradient) of a distance-time graph gives the speed, and the gradient of a displacement-time graph gives the velocity.

平均速率是总距离除以总时间，而瞬时速率是某一时刻的速率。汽车速度表显示的 60 km/h 就是瞬时速率。在图像中，距离-时间图的斜率表示速率，位移-时间图的斜率表示速度。

4. Acceleration | 加速度

Acceleration is the rate of change of velocity. It is a vector quantity and is measured in metres per second squared (m/s²). The acceleration of an object is given by the formula: a = (v – u) / t, where u is the initial velocity, v is the final velocity and t is the time taken. A positive acceleration means the object is speeding up in the positive direction, while a negative acceleration (often called deceleration or retardation) means it is slowing down.

加速度是速度的变化率，它是一个矢量，单位是米每二次方秒 (m/s²)。加速度的计算公式为：a = (v – u) / t，其中 u 是初速度，v 是末速度，t 是所用时间。正加速度表示物体在正方向上加速，负加速度（常称为减速度）表示物体在减速。

It is important not to confuse deceleration with negative acceleration in the opposite direction. If you define the forward direction as positive and the object is moving forward but slowing down, the acceleration is negative. However, if an object is moving in the negative direction and slowing down, the acceleration is actually positive. Always check the sign convention carefully.

注意不要将减速度与相反方向上的负加速度混淆。如果规定前进方向为正，物体向前运动但减速，则加速度为负。但如果物体正沿负方向运动且速度减慢，加速度实际上是正的。务必仔细检查正负号规定。

In a velocity-time graph, the gradient represents acceleration. A straight sloping line indicates constant (uniform) acceleration, while a curved line indicates changing acceleration.

在速度-时间图中，斜率代表加速度。倾斜直线表示恒定（均匀）加速度，曲线则表示加速度在变化。

5. Distance-Time Graphs | 距离-时间图

A distance-time graph plots the distance travelled by an object against the time taken. The key features to remember are: a horizontal line indicates the object is stationary; a straight sloping line shows constant speed; and a curved line indicates changing speed (acceleration or deceleration). The slope (gradient) of the line at any point gives the speed of the object at that instant.

距离-时间图以时间为横轴，距离为纵轴。需要记住的关键特征：水平直线表示物体静止；倾斜直线表示恒定速率；曲线表示速率变化（加速或减速）。线上任一点的斜率给出该时刻的瞬时速率。

To calculate the speed from a distance-time graph, choose two points on a straight section and use the formula: speed = (change in distance) / (change in time). If the graph is curved, you would need to draw a tangent to find the instantaneous speed at a specific time. This is a common skill tested in the IGCSE practical paper.

从距离-时间图计算速率时，选取直线段上的两点，应用公式：速率 = （距离变化）/（时间变化）。如果线是弯曲的，需要画切线来求特定时刻的瞬时速率。这是 IGCSE 实验卷常常考查的技能。

6. Speed-Time Graphs | 速度-时间图

A speed-time graph is one of the most important tools in kinematics. It plots speed on the vertical axis and time on the horizontal axis. A horizontal line means constant speed; a straight sloping line means constant acceleration (or deceleration); a curve means the acceleration is changing. The gradient of the line gives the acceleration, while the area under the graph represents the distance travelled.

速度-时间图是动力学中最重要的工具之一。它以时间为横轴，速度为纵轴。水平直线表示恒定速率；倾斜直线表示恒定加速度（或减速度）；曲线表示加速度在变化。线的斜率给出加速度，而图下的面积代表所走的距离。

When the graph forms a simple shape, such as a rectangle, triangle or trapezium, you can calculate the distance by finding the area geometrically. For a trapezium-shaped graph showing an object accelerating from speed u to speed v in time t, the area = ½ (u + v) t. This directly links to the equations of motion. IGCSE questions often provide a speed-time graph and ask you to find both acceleration and distance, so practise combining gradient and area calculations.

当图形为简单形状，如矩形、三角形或梯形时，可以用几何方法求面积来计算距离。对于表示物体从速度 u 加速到速度 v、用时 t 的梯形图，面积 = ½ (u + v) t。这直接联系到运动方程。IGCSE 题目通常会提供速度-时间图，要求计算加速度和距离，所以要练习结合斜率和面积的计算。

7. Equations of Motion | 运动方程

For objects moving with constant acceleration in a straight line, there are four key equations you must know. These equations link the five variables: initial velocity u, final velocity v, acceleration a, time t and displacement s. The equations are:

对于沿直线做匀加速运动的物体，有四个必须掌握的关键方程。这些方程联系了五个变量：初速度 u、末速度 v、加速度 a、时间 t 和位移 s。方程如下：

1. v = u + at

2. s = ut + ½ at²

3. v² = u² + 2as

4. s = ½ (u + v) t

When solving problems, first identify which three variables you know, then choose the equation that contains these three together with the unknown variable you want to find. Always state the positive direction clearly, and be careful with signs for velocity and acceleration. If an object is slowing down, the acceleration will have the opposite sign to the velocity.

解题时，首先确定已知的三个变量，然后选择含有这三个变量和待求未知量的方程。始终明确正方向，并注意速度和加速度的正负号。如果物体正在减速，加速度的符号将与速度相反。

In the IGCSE examination, these equations will appear in both theory and calculation problems. They are provided on the formula sheet, but you need to know how to apply them correctly. Practise rearranging each equation in terms of different variables so that you can move quickly through the steps in the exam.

在 IGCSE 考试中，这些方程会出现在理论和计算题中。它们会列在公式表上，但你需要知道如何正确应用。练习对每个方程进行不同变量的代换，这样在考试中就能快速完成步骤。

8. Free Fall and Acceleration Due to Gravity | 自由落体与重力加速度

Near the Earth’s surface, all objects fall towards the ground with the same constant acceleration, provided air resistance is negligible. This acceleration due to gravity is denoted by g and has an approximate value of 9.8 m/s². In IGCSE problems, it is often given as 10 m/s² for simplicity. The motion of a freely falling object can be analysed using the equations of motion, with a replaced by g.

在地球表面附近，只要空气阻力可以忽略，所有物体都以相同的恒定加速度下落。这个重力加速度用 g 表示，近似值为 9.8 m/s²。在 IGCSE 题目中，为简化常常取 10 m/s²。自由落体运动可以用运动方程分析，只需将 a 替换为 g。

When an object is thrown vertically upwards, it decelerates at g until it reaches the highest point, where its velocity is momentarily zero. It then accelerates downwards at g. The entire motion is symmetric if air resistance is ignored: the time to go up equals the time to come down, and the speed at any given height is the same going up and coming down.

当物体竖直上抛时，它以 g 减速，直到最高点时速度瞬间为零。然后以 g 向下加速。若忽略空气阻力，整个运动是对称的：上升时间等于下落时间，在某个高度上的速度大小上升和下落时相同。

Typical exam questions involve calculating the time of flight, the maximum height, or the impact speed. Remember to set the correct sign convention: if upward is taken as positive, then the acceleration a = -g. Using the equations of motion with careful substitutions will give the correct answer.

典型考题包括计算飞行时间、最大高度或撞击速度。记住设定正确的正负号规则：如果向上为正，则加速度 a = -g。仔细代入运动方程就能得出正确答案。

9. Practical Skills: Measuring Speed and Acceleration | 实验技能：测量速率和加速度

In the IGCSE physics practical exam, you may be asked to investigate motion using simple apparatus. A common experiment is to measure the speed of a trolley rolling down a ramp. You can use a stopwatch to measure the time taken to travel a known distance, and then calculate the average speed. To find acceleration, you can measure the time to pass between two light gates that record the instantaneous speeds.

在 IGCSE 物理实验考试中，你可能会被要求用简单仪器研究运动。一个常见实验是测量小车沿斜坡下滑的速率。你可以用秒表测量通过已知距离的时间，然后计算平均速率。要测加速度，可以测量通过两个光电门的时间，记录瞬时速度。

A more precise method uses a ticker-tape timer, which makes dots on a paper tape at a fixed frequency (often 50 Hz, so dots are 0.02 s apart). By analysing the distance between successive dots, you can determine whether the speed is constant, increasing or decreasing, and you can calculate average speed and acceleration. Remember: for a frequency of 50 Hz, the time for one dot interval is 0.02 s.

更精确的方法是用打点计时器，它以固定频率（通常 50 Hz，因此点间隔 0.02 s）在纸带上打点。通过分析相邻点之间的距离，可以判断速度是恒定、增大还是减小，并能计算平均速率和加速度。记住：50 Hz 频率下，一个点间隔的时间是 0.02 s。

When plotting a graph of speed against time from such data, always label axes clearly, choose sensible scales, and draw a best-fit line. The gradient of this line gives the acceleration. Be prepared to describe how to reduce experimental error, such as repeating measurements and taking an average.

根据这些数据绘制速度-时间图时，要始终清楚地标注坐标轴，选择合适比例，并画出最佳拟合线。线的斜率就是加速度。还要会描述如何减少实验误差，例如重复测量取平均值。

10. Motion in a Straight Line: Key Formulae and Sign Convention | 直线运动：关键公式与符号规则

Throughout kinematics problems, maintaining a consistent sign convention is essential. Start by defining one direction as positive. All vectors in that direction are positive, and those opposite are negative. This applies to displacement, velocity and acceleration. A common mistake is to use different sign rules in the same problem, which leads to incorrect answers.

在整个动力学问题中，保持一致的正负号规则至关重要。首先规定一个方向为正。所有沿该方向的矢量都为正，相反的为负。这适用于位移、速度和加速度。常见错误是在同一问题中混用不同的符号规则，导致错误答案。

Here is a summary of the key formulas you need to memorise, even though they appear on the formula sheet:

以下是需要记住的关键公式总结，尽管公式表上会提供：

Quantity 量	Formula 公式
Speed 速率	v = d / t
Acceleration 加速度	a = (v – u) / t
v = u + at	–
s = ut + ½ at²	–
v² = u² + 2as	–
s = ½ (u + v) t	–

Remember to use these equations only when acceleration is constant. If acceleration is not constant, you must use graphical methods (area under speed-time graph for distance, gradient for acceleration) or more advanced techniques that are not required at IGCSE level.

切记只有加速度恒定时才能使用这些方程。如果加速度不是恒定的，必须使用图像法（速度-时间图下面积求距离，斜率求加速度）或更高级的方法，但这些不在 IGCSE 要求范围内。

11. Interpreting Complex Motion Graphs | 解读复杂运动图像

Some IGCSE questions will present a graph that combines several types of motion. A speed-time graph might show an initial period of acceleration, followed by constant speed, and then deceleration to rest. You must be able to describe each section in words and calculate the total distance travelled by adding the areas under each part.

一些 IGCSE 题目会给出结合几种运动类型的图像。速度-时间图可能显示先加速、再匀速、然后减速至静止。你必须能够用文字描述每段运动，并通过将各部分下的面积相加计算总路程。

For displacement-time graphs, a curve that flattens out indicates the object is slowing down and stopping. A curve becoming steeper shows speeding up. The gradient at any point is the instantaneous velocity. Understanding the shape and meaning of these graphs is a highly examinable skill.

对于位移-时间图，曲线趋于平缓表示物体在减速并停止，曲线变陡表示加速。任一点的斜率都是瞬时速度。理解这些图形的形状和含义是一项非常容易考查的技能。

When a question asks you to ‘describe the motion’, you should use phrases such as ‘constant positive velocity’, ‘constant acceleration’, ‘decelerating uniformly’, and refer to the sections of the graph by time intervals. Avoid vague language like ‘the line goes up’.

当题目要求“描述运动”时，应该使用“恒定的正速度”、“恒定加速度”、“匀减速”等短语，并按时间区间来说明图像的各个部分。避免“线向上走”这样的模糊表述。

12. Exam Tips and Common Pitfalls | 考试技巧与常见误区

Finally, here are some essential tips to perform well in the kinematics section of CIE IGCSE Physics. First, always write down the known quantities and the unknown before choosing an equation. Second, check that all quantities are in SI units: metres, seconds, metres per second, etc. Convert kilometres to metres and minutes to seconds if necessary.

最后，这里有一些在 CIE IGCSE 物理动力学部分取得好成绩的关键技巧。首先，在选方程之前，总是先写下已知量和未知量。其次，检查所有物理量是否使用国际单位：米、秒、米每秒等。必要时将公里转换为米，分钟转换为秒。

Third, when calculating an area under a speed-time graph, always check whether the shape is a simple polygon. If it is a combination of a rectangle and a triangle, work them out separately and add. Fourth, never forget to include the unit in your final answer; a number without a unit is meaningless in physics. Fifth, if a question asks for displacement and your calculation gives a negative result, do not panic – this simply means the displacement is in the opposite direction to your chosen positive.

第三，在计算速度-时间图下面积时，始终检查形状是否为简单多边形。如果是矩形和三角形的组合，分别计算然后相加。第四，永远不要忘记在最终答案中写上单位；没有单位的数字在物理中没有意义。第五，如果题目要求求位移而你的计算得到负值，不要慌张——这只是意味着位移方向与你选定的正方向相反。

Practise past paper questions under timed conditions to get used to the type of kinematics problems that appear. Many students lose marks by confusing distance-time and speed-time graphs, so draw a quick sketch to remind yourself which graph you are dealing with. With consistent practice and careful attention to signs, you can score full marks on this topic.

在限时条件下练习历年真题，熟悉出现的动力学问题类型。许多学生因为混淆距离-时间图和速度-时间图而丢分，因此画一个简单草图提醒自己正在处理哪种图像。通过持续练习和对符号的仔细关注，你完全可以在这个主题上拿到满分。

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IGCSE CIE Physics: Kinematics Revision | IGCSE CIE 物理：动力学 考点精讲