📚 IGCSE Maths Motion Graphs: Distance-Time and Speed-Time Graphs | IGCSE数学运动图线：距离-时间图与速度-时间图
Motion graphs are one of the most practical topics in IGCSE Maths. They connect algebraic ideas such as gradient, area and units with real-life movement, so exam questions often test several skills at the same time.
运动图线是IGCSE数学中最实用的主题之一。它把斜率、面积和单位等代数概念与真实运动联系起来，因此考试题经常同时考查多个技能。
In this article, you will learn how to read both distance-time and speed-time graphs, calculate speed, acceleration and distance, and avoid common exam mistakes.
在本文中，你将学会如何读懂距离-时间图和速度-时间图，计算速度、加速度和路程，并避开常见考试误区。
1. What Are Motion Graphs? | 什么是运动图线？
A motion graph shows how one movement quantity changes with time. The two main types in IGCSE are the distance-time graph and the speed-time graph.
运动图线表示某个运动量如何随时间变化。IGCSE中主要考两种图：距离-时间图和速度-时间图。
The horizontal axis is almost always time. The vertical axis is either distance from a starting point or speed. Always check the axis label before answering.
横轴几乎总是时间。纵轴要么是离起点的距离，要么是速度。答题前一定要先确认坐标轴标签。
- Distance-time graph: vertical axis = distance travelled.
- 距离-时间图：纵轴 = 已走距离。
- Speed-time graph: vertical axis = speed.
- 速度-时间图：纵轴 = 速度。
2. Reading a Distance-Time Graph | 读懂距离-时间图
In a distance-time graph, the shape of the line tells you how the object is moving.
在距离-时间图中，线的形状告诉你物体的运动方式。
- A horizontal line means the object is stationary.
- 水平线表示物体静止。
- A straight line with a positive gradient means constant speed away from the start.
- 正斜率的直线表示物体以恒定速度远离起点。
- A straight line with a negative gradient means constant speed back towards the start.
- 负斜率的直线表示物体以恒定速度返回起点。
- A curved line means the speed is changing, so the object is accelerating or decelerating.
- 曲线表示速度正在变化，因此物体在加速或减速。
The steeper the line, the greater the speed. A gentle slope means lower speed.
线越陡，速度越大。平缓的坡度表示速度较低。
3. Speed from a Distance-Time Graph | 从距离-时间图求速度
Speed is found from the gradient of a distance-time graph. For a straight section, use the change in distance divided by the change in time.
速度由距离-时间图的斜率求得。对于直线段，用距离变化量除以时间变化量。
speed = Δdistance ÷ Δtime
If the distance is in metres and time is in seconds, speed is in m/s. If distance is in km and time is in hours, speed is in km/h.
如果距离以米为单位、时间以秒为单位，速度单位是米/秒。如果距离以千米为单位、时间以小时为单位，速度单位是千米/时。
Average speed uses total distance divided by total time, not the average of two speeds unless the time intervals are equal.
平均速度用总距离除以总时间，而不是两个速度的平均值，除非时间间隔相等。
4. Reading a Speed-Time Graph | 读懂速度-时间图
In a speed-time graph, the vertical height shows the speed at any moment. The gradient tells you about acceleration.
在速度-时间图中，纵轴高度表示任意时刻的速度。斜率告诉你加速度信息。
- A horizontal line means constant speed.
- 水平线表示恒定速度。
- A positive gradient means increasing speed, so the object is accelerating.
- 正斜率表示速度增加，因此物体在加速。
- A negative gradient means decreasing speed, so the object is decelerating.
- 负斜率表示速度减小，因此物体在减速。
If the line touches the time axis, the speed is zero, meaning the object has stopped.
如果图线接触时间轴，速度为零，说明物体已经停下。
5. Acceleration from a Speed-Time Graph | 从速度-时间图求加速度
Acceleration is the gradient of a speed-time graph. Use the change in speed divided by the time taken.
加速度是速度-时间图的斜率。用速度变化量除以所用时间。
acceleration = Δv ÷ Δt = (v₂ − v₁) ÷ (t₂ − t₁)
For deceleration, the gradient is negative. In IGCSE answers, you can state the magnitude of deceleration as a positive value, for example 4 m/s².
减速时斜率为负。在IGCSE答案中，你可以把减速度的大小写成正值，例如4 m/s²。
Always include units, normally m/s² when speed is in m/s and time is in seconds.
一定要写单位。当速度单位是米/秒、时间单位是秒时，加速度单位通常是米/秒²。
6. Area under a Speed-Time Graph | 速度-时间图下的面积
The area between a speed-time graph and the time axis gives the total distance travelled.
速度-时间图与时间轴之间的面积等于总行驶距离。
Divide the area into simple shapes such as rectangles, triangles and trapezia, then find the total area.
把面积分成矩形、三角形和梯形等简单图形，然后求总面积。
- Rectangle area = length × width
- 矩形面积 = 长 × 宽
- Triangle area = ½ × base × height
- 三角形面积 = ½ × 底 × 高
- Trapezium area = ½ × (sum of parallel sides) × height
- 梯形面积 = ½ × （两平行边之和）× 高
If the graph goes below the time axis, this is not needed in most IGCSE Maths questions; IGCSE mainly uses positive speed.
如果图线延伸到时间轴下方，多数IGCSE数学题不需要处理；IGCSE主要使用正速度。
7. Common Exam Misconceptions | 常见考试误区
- Confusing distance-time and speed-time graphs. In a distance-time graph, the gradient gives speed. In a speed-time graph, the area gives distance.
- 混淆距离-时间图和速度-时间图。在距离-时间图中，斜率给出速度。在速度-时间图中，面积给出距离。
- Reading the height of a distance-time graph as speed. The height is distance, not speed.
- 把距离-时间图的纵轴高度误读为速度。纵轴高度是距离，不是速度。
- Forgetting to check the scale on each axis before calculating gradient or area.
- 计算斜率或面积前忘记检查每个坐标轴的刻度。
- Mixing units, such as using seconds with km without converting.
- 混用单位，例如秒与千米不换算就直接使用。
- Using average of speeds instead of total distance divided by total time for average speed.
- 求平均速度时使用速度平均，而不是用总距离除以总时间。
8. Worked Example | 典型例题
Example 1: An athlete runs 300 m in 30 s, stops for 10 s, then runs back 300 m in 60 s. Find the speed for each moving part and the average speed for the whole journey.
例题1：一名运动员在30秒内跑300米，休息10秒，然后在60秒内跑回300米。求每段运动的速度以及全程平均速度。
First part speed = 300 m ÷ 30 s = 10 m/s.
第一段速度 = 300 m ÷ 30 s = 10 m/s。
Return speed = 300 m ÷ 60 s = 5 m/s.
返回速度 = 300 m ÷ 60 s = 5 m/s。
m = 600 m. Total time = 30 s + 10 s + 60 s = 100 s. Average speed = 600 m ÷ 100 s = 6 m/s.
总距离 = 300 m + 300 m = 600 m。总时间 = 30 s + 10 s + 60 s = 100 s。平均速度 = 600 m ÷ 100 s = 6 m/s。
Example 2: A lorry accelerates from rest to 20 m/s in 10 s, holds 20 m/s for 30 s, then decelerates to rest in 20 s. Find the total distance travelled.
例题2：一辆货车从静止开始，在10秒内加速到20 m/s，保持20 m/s行驶30秒，然后在20秒内减速到静止。求总行驶距离。
The area under the speed-time graph is made of a triangle, a rectangle and another triangle.
速度-时间图下的面积由一个三角形、一个矩形和另一个三角形组成。
Area = ½ × 10 × 20 + 30 × 20 + ½ × 20 × 20
Area = 100 + 600 + 200 = 900 m
The total distance is 900 m. This type of 900 m journey problem is common in IGCSE practice and revision books.
总距离为900米。这类900米行程问题在IGCSE练习与复习用书中很常见。
9. Exam-Style Checklist | 考试答题清单
- Read the axis labels and units first.
- 先读坐标轴标签和单位。
- Identify whether the graph is distance-time or speed-time.
- 判断图是距离-时间图还是速度-时间图。
- For distance-time graphs, use gradient for speed.
- 对距离-时间图，用斜率求速度。
- For speed-time graphs, use gradient for acceleration and area for distance.
- 对速度-时间图，用斜率求加速度，用面积求距离。
- Show all working and include units in the final answer.
- 展示所有步骤，并在最终答案中写出单位。
- Check whether the question asks for average speed or instantaneous speed.
- 检查题目问的是平均速度还是瞬时速度。
10. Summary of Key Formulae and Graph Meanings | 核心公式与图线含义总结
| Graph type | Gradient gives | Area gives |
| Distance-time graph | speed | not usually used |
| Speed-time graph | acceleration | distance travelled |
核心公式如下：
speed = Δdistance ÷ Δtime
acceleration = Δv ÷ Δt
distance = area under speed-time graph
These three relationships solve most IGCSE motion graph questions. Master them and practise dividing non-standard areas into rectangles and triangles.
这三个关系能解决大多数IGCSE运动图线题。掌握它们，并练习把不规则面积分成矩形和三角形。
Published by TutorHao | IGCSE Maths Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图