📚 Motion Graphs: Distance-Time and Speed-Time Graphs for IGCSE Maths | IGCSE 数学运动图像：距离-时间图与速度-时间图
Understanding motion graphs is a core skill in IGCSE Mathematics. Whether you are interpreting a distance-time graph or calculating acceleration from a speed-time graph, the key is to link the gradient and the area under the graph to real movement.
理解运动图像是 IGCSE 数学的核心技能。无论是解读距离-时间图，还是从速度-时间图中计算加速度，关键都是将图像的斜率和图像下的面积与实际运动联系起来。
This article covers the essential definitions, interpretations, worked examples and common exam pitfalls for both distance-time and speed-time graphs. Teachers can use it as a structured revision resource, and students can use it as a self-study checklist.
本文涵盖距离-时间图和速度-时间图的基本定义、图像解读、典型例题和常见考试易错点。教师可将其作为结构化的复习资源，学生可将其作为自学清单。
1. The Two Main Motion Graphs | 两种主要的运动图像
In IGCSE Maths, two graphs dominate motion questions: the distance-time graph and the speed-time graph. They look similar but give different information.
在 IGCSE 数学中，有两种图像主导运动问题：距离-时间图和速度-时间图。它们看起来相似，但提供的信息不同。
A distance-time graph plots total distance from a fixed starting point against time. A speed-time graph plots how the speed of an object changes over time.
距离-时间图表示物体离固定起点的总距离随时间的变化。速度-时间图表示物体的速度随时间的变化。
The gradient of a distance-time graph gives speed, while the gradient of a speed-time graph gives acceleration. The area under a speed-time graph gives the total distance travelled.
距离-时间图的斜率给出速度，而速度-时间图的斜率给出加速度。速度-时间图下方的面积给出总行驶距离。
2. Distance-Time Graphs: Reading the Story | 距离-时间图：读出运动过程
On a distance-time graph, the horizontal axis is time and the vertical axis is distance from the start. The shape of the line tells you exactly what is happening.
在距离-时间图中，横轴是时间，纵轴是离起点的距离。线的形状能准确地告诉你正在发生什么。
A horizontal line means the object is stationary: the distance does not change as time passes. A straight sloping line means constant speed, and the steeper the line, the greater the speed.
水平线表示物体静止：距离不随时间变化。倾斜的直线表示匀速运动，线越陡，速度越大。
A curved line means the speed is changing. A curve that gets steeper shows acceleration, while a curve that levels off shows deceleration.
曲线表示速度在变化。曲线变陡表示加速，曲线趋于平缓表示减速。
For a distance-time graph, the gradient formula is:
speed = Δdistance ÷ Δtime
对于距离-时间图，斜率公式为：速度 = 距离变化量 ÷ 时间变化量。
3. Speed-Time Graphs: Reading the Story | 速度-时间图：读出运动过程
A speed-time graph has time on the horizontal axis and speed on the vertical axis. It is especially useful for analysing acceleration and distance travelled.
速度-时间图以时间为横轴，速度为纵轴。它特别适合分析加速度和行驶距离。
A horizontal line on a speed-time graph means constant speed: the speed is not changing. A straight sloping line upwards means uniform acceleration, and a straight sloping line downwards means uniform deceleration.
速度-时间图上的水平线表示匀速：速度不变。向上倾斜的直线表示匀加速，向下倾斜的直线表示匀减速。
A curved line means the acceleration is changing. This is more common in real-life motion, such as a car gradually building up speed in traffic.
曲线表示加速度在变化。这在现实生活中更常见，例如汽车在交通中逐渐加速。
4. Gradient on Speed-Time Graphs: Acceleration | 速度-时间图的斜率：加速度
On a speed-time graph, the gradient tells you the acceleration. A positive gradient means positive acceleration, a negative gradient means deceleration, and a zero gradient means constant speed.
在速度-时间图中，斜率表示加速度。正斜率表示正加速度，负斜率表示减速，斜率为零表示匀速。
Acceleration is calculated as the change in speed divided by the time taken. The formula is:
加速度计算为速度变化量除以所用时间。公式为：
a = (v − u) ÷ t
其中 a 是加速度，v 是末速度，u 是初速度，t 是时间。
In IGCSE questions, acceleration is usually measured in m/s². Always check the units before substituting values.
在 IGCSE 题目中，加速度通常以 m/s² 为单位。代入数值前务必检查单位。
5. Area Under a Speed-Time Graph: Distance | 速度-时间图下的面积：距离
The area between a speed-time graph and the time axis represents the distance travelled. This is one of the most important results in IGCSE motion questions.
速度-时间图与时间轴之间的面积表示行驶距离。这是 IGCSE 运动问题中最重要的结论之一。
d × time. For a uniformly accelerating section, the area may be a triangle or a trapezium.
对于匀速段，面积是矩形，因此距离 = 速度 × 时间。对于匀加速段，面积可能是三角形或梯形。
height. For a trapezium, use area = ½ × (a + b) × h, where a and b are the parallel sides.
对于三角形，使用面积 = ½ × 底 × 高。对于梯形，使用面积 = ½ × (上底 + 下底) × 高，其中 a 和 b 是两条平行边。
le is time and the height is change in speed. The units work out correctly because m/s × s
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