📚 GCSE CIE Maths: Mechanics Revision Guide | GCSE CIE 数学：力学 考点精讲
Mechanics, specifically kinematics, forms an integral part of the CIE IGCSE Mathematics syllabus (0580). It covers the study of motion, including speed, velocity, acceleration, and the mathematical relationships that link distance, time, and speed. A strong grasp of this topic not only secures marks in the exam but also provides a solid foundation for A-Level Mathematics and Physics. This guide will walk you through all the essential concepts, equations, and graph skills you need to confidently tackle mechanics questions.
力学——更准确地说是运动学——是 CIE IGCSE 数学（0580）大纲的重要组成部分。它研究运动中的速率、速度、加速度以及距离、时间与速度之间的数学关系。扎实掌握这个专题不仅能帮你稳稳拿下考试分数，还为 A Level 数学与物理打下坚实的基础。本指南将带你逐一梳理所有核心概念、方程和图像技巧，让你自信面对力学题目。
1. Scalars and Vectors | 标量与矢量
Quantities in mechanics are classified as either scalars or vectors. Scalars possess only magnitude (size), such as speed (50 km/h) and distance (100 m). Vectors have both magnitude and direction, like velocity (50 km/h north) and displacement (100 m east). This distinction is critical because vectors must be added or subtracted with direction in mind, while scalars simply add numerically. Exam questions frequently test your ability to tell apart distance (scalar) and displacement (vector), or speed and velocity.
力学中的物理量分为标量和矢量。标量只有大小，如速率（50 km/h）和距离（100 m）。矢量既有大小又有方向，如速度（50 km/h 向北）和位移（100 m 向东）。这一区别至关重要，因为矢量相加减时必须考虑方向，而标量直接进行数值相加。考试中经常考查是否能够区分距离（标量）与位移（矢量），或者速率与速度。
2. Speed, Velocity and Acceleration | 速率、速度与加速度
epresents initial velocity, v final velocity, and t the time taken. Standard SI units are metres per second (m/s) for velocity and metres per second squared (m/s²) for acceleration. A positive a indicates speeding up; a negative a (deceleration) means slowing down. In CIE IGCSE Maths, motion is usually considered with constant acceleration.
速率是距离的变化率，公式为 速率 = 距离 ÷ 时间。作为矢量的速度则是位移的变化率。加速度用于衡量速度变化的快慢，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。标准国际单位是 m/s（速度）和 m/s²（加速度）。a 为正表示加速，a 为负（减速度）表示减速。在 CIE IGCSE 数学范围内，通常研究匀加速度下的运动。
3. Distance–Time Graphs | 距离–时间图
A distance-time graph plots the total distance travelled against time. The gradient of the line tells us the speed. A straight line means constant speed, while a horizontal line indicates the object is stationary. A curved line shows changing speed (acceleration or deceleration). To find the speed at a specific point on a curve, draw a tangent at that point and calculate its gradient. Average speed over a journey is simply total distance divided by total time.
距离–时间图描绘了行驶的总距离如何随时间变化。图线的梯度（斜率）代表速率。直线表示匀速运动，水平线则代表物体静止。曲线代表速率发生变化（加速或减速）。若要找出曲线上某一点的速率，就在该点处作一条切线，然后计算这条切线的斜率。整个行程的平均速率等于总距离除以总时间。
4. Speed–Time Graphs | 速度–时间图
A speed-time graph (or velocity-time graph) is an extremely powerful tool. The gradient of the line gives the acceleration. A horizontal line represents constant speed; an upward-sloping straight line means constant acceleration; a downward-sloping line indicates deceleration. Crucially, the area under the graph represents the distance travelled. Common shapes are triangles, rectangles, and trapeziums. You must be comfortable with splitting the area into these simple shapes to find the total distance.
速度–时间图是一个极为强大的工具。图线的梯度代表加速度。水平线表示匀速运动，向上倾斜的直线表示匀加速，向下倾斜的直线表示匀减速。最关键的一点是，图线与时间轴围成的面积代表物体行驶的距离。常见图形包括三角形、矩形和梯形。你必须熟练地将区域拆分成这些简单形状，从而求出总距离。
5. Equations of Motion (SUVAT) | 匀加速运动方程 (SUVAT)
. These equations appear on the CIE IGCSE formula sheet, but you must know how to select and apply the right one.
对于直线上的匀加速运动，有四个基本方程，常被称为 SUVAT 方程。符号约定如下：s = 位移，u = 初速度，v = 末速度，a = 加速度，t = 时间。这些方程会出现在 CIE IGCSE 的公式表上，但你必须懂得如何选择并正确运用它们。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
example, if t is not needed, use v² = u² + 2as. Consistent units are essential throughout.
使用这些方程时，先列出已知量和待求量，然后挑选一个不包含多余未知量的方程。例如，若不需要用到时间 t，就选用 v² = u² + 2as。整个过程必须保持单位一致。
| Equation | 中文表达 | Missing variable |
|---|---|---|
| v = u + at | v = u + at | s |
| s = ut + ½at² | s = ut + ½at² | v |
| v² = u² + 2as | v² = u² + 2as | t |
| s = ½(u + v)t | s = ½(u + v)t | a |
6. Applying SUVAT Equations | 运用 SUVAT 方程
Let' ply s = ½(u + v)t = ½(0+10)×5 = 25 m. When an object decelerates, remember to make a negative. In vertical motion under gravity, a is usually 9.8 m/s² downwards, but its sign depends on your chosen positive direction.
来看一个典型例子：一辆汽车从静止（u = 0）开始，以 2 m/s² 的加速度行驶 5 秒钟。求行驶距离。已知：u = 0, a = 2, t = 5；未知量 s。最直接的方程是 s = ut + ½at² = 0×5 + ½×2×5² = 25 m。或者，你也可以先求出 v = u + at = 0 + 2×5 = 10 m/s，再代入 s = ½(u + v)t = ½(0+10)×5 = 25 m。若物体减速，记得让 a 取负值。在重力作用下的竖直运动中，a 通常取 9.8 m/s² 向下，但符号的正负取决于你设定的正方向。
7. Interpreting Graphs: Gradients and Areas | 解读图像：斜率和面积
ds to be split into rectangles (width × height), triangles (½ × base × height), or trapeziums (½ × sum of parallel sides × height). Even when the graph is a single straight line, the area under it follows the same geometry rules.
要准确解读力学图像，你必须熟练计算直线段构成的斜率和面积。斜率 = 垂直变化 / 水平变化。在距离–时间图上，斜率 = 速率；在速度–时间图上，斜率 = 加速度。速度–时间图下的面积通常需要拆分为矩形（宽 × 高）、三角形（½ × 底 × 高）或梯形（½ × 平行边之和 × 高）。即使整个图线只是一条直线，其下方的面积仍遵循相同的几何法则。
8. Converting Units | 单位换算
xample, 54 km/h becomes 54 ÷ 3.6 = 15 m/s. Similarly, convert minutes to seconds by multiplying by 60. Once all values are in SI units, the SUVAT equations will work correctly.
力学中最常见的错误之一就是单位混用。题目可能给出以 km/h 为单位的速度、以米为单位的距离和以秒为单位的时间
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