📚 738: Forces and Motion – Speed, Velocity and Acceleration | 力与运动 - 速率、速度与加速度
In the Edexcel IGCSE Science syllabus, Topic 738 introduces the core ideas of kinematics – the study of how objects move. This article unpacks the essential differences between speed, velocity and acceleration, and shows you how to describe motion using graphs and equations. Understanding these concepts is fundamental not only for the Physics paper but also for interpreting real-world motion in everyday life.
在Edexcel IGCSE科学课程大纲中，主题738引入了运动学的核心概念——研究物体如何运动。本文详细解析速率、速度和加速度之间的本质区别，并展示如何利用图形和方程描述运动。理解这些概念不仅是物理试卷的基础，也是解读日常生活中物体运动的关键。
1. Defining Motion | 运动的定义
Motion occurs when an object changes its position with respect to a reference point. In physics, we describe motion using measurable quantities such as distance travelled, displacement, speed, velocity and acceleration. A full description requires both the magnitude (how much) and, for some quantities, the direction of movement. The simplest form of motion is along a straight line, which we call linear motion.
当物体相对于参考点改变位置时，就发生了运动。在物理学中，我们使用可测量的量来描述运动，例如移动路程、位移、速率、速度和加速度。完整的描述需要大小（多少），而对于某些量还需要运动方向。最简单的运动形式是沿直线进行的，我们称之为直线运动。
2. Scalar and Vector Quantities | 标量与矢量
Quantities in physics are split into two categories: scalars and vectors. Scalars have only magnitude (size), while vectors have both magnitude and direction. This distinction is crucial when we talk about speed and velocity. Distance is a scalar, displacement is a vector. Mistaking speed for velocity is one of the most common errors at IGCSE level.
物理量分为两类：标量和矢量。标量只有大小，而矢量既有大小又有方向。当我们讨论速率和速度时，这一区别至关重要。路程是标量，位移是矢量。把速率当作速度是IGCSE阶段最常见的错误之一。
| Scalars (magnitude only) | 标量（仅大小） | Vectors (magnitude + direction) | 矢量（大小+方向） |
|---|---|
| Distance | 路程 | Displacement | 位移 |
| Speed | 速率 | Velocity | 速度 |
| Mass | 质量 | Weight | 重量 |
| Time | 时间 | Acceleration | 加速度 |
3. Speed as a Scalar | 速率作为标量
Speed is defined as the distance travelled per unit time. It does not depend on direction. The formula is: speed = distance ÷ time. The SI unit of speed is metres per second (m/s). If a runner completes 400 m in 50 s, their average speed is 8 m/s, regardless of the track's shape. In everyday language, we often use 'speed' when we actually mean 'velocity', but in physics the difference matters.
速率定义为单位时间内移动的路程。它与方向无关。公式是：速率 = 路程 ÷ 时间。速率的国际单位是米每秒（m/s）。如果一名跑步者在50秒内跑完400米，他的平均速率为8 m/s，无论跑道形状如何。在日常语言中，我们常把“速率”用作“速度”，但在物理学中，二者的差异很重要。
4. Velocity as a Vector | 速度作为矢量
Velocity is speed in a given direction. It is calculated as displacement divided by time: velocity = displacement ÷ time. Because it is a vector, velocity can be positive or negative to indicate direction. For example, a car travelling 20 m/s north has a different velocity from one travelling 20 m/s south, even though their speeds are identical. Uniform motion with constant velocity means both steady speed and unchanging direction.
速度是给定方向上的速率。它由位移除以时间计算：速度 = 位移 ÷ 时间。由于速度是矢量，它可以取正值或负值以表示方向。例如，一辆汽车以20 m/s向北行驶，与一辆以20 m/s向南行驶的速度不同，尽管它们的速率相同。匀速直线运动意味着速率稳定且方向不变。
5. Acceleration: The Rate of Change of Velocity | 加速度：速度变化率
Acceleration tells us how quickly velocity changes. It is a vector quantity defined as change in velocity per unit time: a = Δv / t, where Δv is the final velocity minus initial velocity (v − u). The SI unit is m/s². An object accelerates if its speed changes, or if its direction changes (as in circular motion). Negative acceleration is often called deceleration or retardation, and it indicates the object is slowing down.
加速度表示速度变化的快慢。它是矢量，定义为单位时间内速度的变化量：a = Δv / t，其中Δv是末速度减去初速度（v − u）。国际单位是米每二次方秒（m/s²）。如果物体的速率改变，或者方向改变（如圆周运动），它都在加速。负加速度常被称为减速度，表示物体正在减慢。
6. Equations of Motion | 运动方程
For uniform acceleration in a straight line, four key equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). They are only valid when acceleration is constant. The equations are:
对于匀加速直线运动，有四个关键方程将位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t) 联系起来。它们仅在加速度恒定时有效。方程如下：
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = (u + v) t / 2
Memorising these and knowing when to use each is vital for solving kinematic problems. Remember to assign directions, e.g. upward as positive, so downward acceleration becomes negative (−9.8 m/s²).
熟记这些方程并知道何时使用每个方程，对于解决运动学问题至关重要。记住要设定方向，例如向上为正，这样向下的加速度就是负值（−9.8 m/s²）。
7. Distance–Time Graphs | 距离–时间图
A distance–time graph plots distance travelled on the y-axis against time on the x-axis. The slope (gradient) of the line gives the speed. A straight line indicates constant speed; a horizontal line means the object is stationary. A curved line tells us the speed is changing, and the gradient at any point equals the instantaneous speed.
距离–时间图将行进路程作为纵轴，时间作为横轴绘制。线的斜率（梯度）给出速率。直线表示匀速；水平线意味着物体静止。曲线告诉我们速率在变化，任意一点的梯度等于瞬时速率。
8. Velocity–Time Graphs | 速度–时间图
Velocity–time graphs are even more powerful. The gradient of a velocity–time graph gives acceleration. A horizontal line corresponds to constant velocity; a sloping straight line indicates constant acceleration. The area under the graph represents the displacement (or distance if direction is constant). A line crossing the time axis shows a change in direction.
速度–时间图更具威力。速度–时间图的梯度给出加速度。水平线对应恒定速度；倾斜直线表示匀加速度。图线下方的面积代表位移（若方向不变则为路程）。穿过时间轴的一条线表示方向改变。
9. Calculating Acceleration from Graphs | 从图中计算加速度
To find acceleration from a velocity–time graph, pick two points on the straight section and calculate acceleration = (v – u) / t, which is the rise over run. For non-uniform acceleration where the line curves, draw a tangent at the point of interest and find its gradient. This method gives instantaneous acceleration. Examiners often ask you to determine if acceleration is increasing or decreasing based on the gradient's steepening or flattening.
要从速度–时间图求加速度，选取直线部分上的两点，计算加速度 = (v – u) / t，即纵差横差。对于线弯曲的非匀加速度情况，在感兴趣的点画切线并求其梯度。这种方法给出瞬时加速度。考官常要求根据梯度的陡缓判断加速度是在增大还是减小。
10. Uniform and Non-uniform Motion | 匀速与非匀速运动
Uniform motion implies constant velocity – a single straight line in both distance–time and velocity–time graphs (though on a velocity–time graph a constant velocity shows as a horizontal line). Non-uniform motion means changing speed or direction. An object falling freely under gravity approximates uniform acceleration (ignoring air resistance) and produces a sloping straight line on a velocity–time graph. Understanding these patterns allows you to predict future motion.
匀速运动意味着恒定速度——在距离–时间图和速度–时间图中都是单一直线（但在速度–时间图上，恒定速度表现为水平线）。非匀速运动意味着速率或方向在改变。物体在重力作用下自由下落可近似为匀加速运动（忽略空气阻力），其在速度–时间图上产生一条倾斜直线。理解这些图样能让你预测未来的运动。
11. Practical Applications | 实际应用
These concepts are not just academic. Sport scientists use velocity data to analyse sprinters' performances. Car manufacturers design safety systems based on acceleration limits. Speed cameras measure instant speed, and navigation apps use velocity vectors to predict arrival times. Even everyday phrases like 'I was doing 30 miles per hour' involve speed, not velocity, because direction is omitted.
这些概念不仅有学术意义。体育科学家使用速度数据分析短跑运动员的表现。汽车制造商根据加速度极限设计安全系统。测速摄像头测量瞬时速率，导航应用利用速度矢量预测到达时间。就连日常所说的“我开到了30英里每小时”也涉及的是速率而非速度，因为省略了方向。
12. Exam Tips for Edexcel IGCSE Topic 738 | Edexcel IGCSE主题738的考试技巧
When answering questions on motion, always state whether you are calculating speed or velocity, and include units. For equations of motion, list the known quantities and choose the equation that contains only one unknown. Use a ruler to read graphs and show your working clearly. Practice converting units, such as km/h to m/s (divide by 3.6). If a question mentions 'uniform acceleration', you can trust the SUVAT equations; if not, rely on distance–time or velocity–time graphs.
在回答运动类问题时，务必说明你计算的是速率还是速度，并标注单位。使用运动方程时，列出已知量并选择只含一个未知数的方程。用直尺读取图表，并清楚地展示计算步骤。练习单位换算，如将 km/h 转换为 m/s（除以3.6）。如果题目提到“匀加速度”，你可以信赖 SUVAT 方程；否则，需借助距离–时间或速度–时间图。
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