📚 Distance-Time Graphs and Speed Calculations | 距离-时间图与速度计算
Distance-time graphs show how an object's distance changes over time. They are a key part of the Cambridge KS3 Mathematics curriculum, especially when studying graphs, ratio and speed.
距离-时间图显示物体的距离如何随时间变化。这是剑桥 KS3 数学课程中关于图像、比和速度的重要考点。
In this article, you will learn how to read, interpret and draw distance-time graphs, and how to calculate speed from the slope of a line.
在本文中，你将学习如何读取、解释和绘制距离-时间图，以及如何从线段的斜率计算速度。
1. What is a Distance-Time Graph? | 什么是距离-时间图？
A distance-time graph plots distance on the vertical y-axis and time on the horizontal x-axis. Each point on the graph tells you how far an object has travelled from its starting point at a particular time.
距离-时间图在竖直的 y 轴上表示距离，在水平的 x 轴上表示时间。图上的每个点告诉你物体在某一特定时间时距起点已经走了多远。
The graph combines two variables: distance travelled and time elapsed. In KS3 Mathematics, you normally use straight line segments to show constant speed, rest or return journeys.
这张图结合了两个变量：走过的距离和经过的时间。在 KS3 数学中，通常使用直线段来表示匀速、静止或返程。
2. Reading a Distance-Time Graph | 如何读取距离-时间图
To read a point, move up from the time value on the x-axis until you hit the graph, then move across to the y-axis to read the distance. For example, the point (5, 25) means that after 5 seconds, the object is 25 metres from the start.
读取一个点的方法是：从 x 轴上的时间值向上移动到图像，然后水平移到 y 轴读取距离。例如，点 (5, 25) 表示 5 秒后物体距起点 25 米。
Always check the units on both axes before you start. The time axis might be in seconds, minutes or hours, while the distance axis might be in metres or kilometres.
开始前一定要检查两个轴上的单位。时间轴可能以秒、分钟或小时为单位，而距离轴可能以米或千米为单位。
3. Slope and Speed | 斜率与速度
The slope, or gradient, of a distance-time graph tells you the speed of the object. A steeper line means a higher speed, because the distance is increasing more quickly for the same amount of time.
距离-时间图的斜率（也叫坡度）告诉你物体的速度。直线越陡，速度越高，因为在相同时间内距离增加得更快。
The gradient is calculated by dividing the change in distance by the change in time. This is exactly the same as the formula for speed.
斜率的计算方法是用距离的变化量除以时间的变化量。这与速度公式完全相同。
speed = Δdistance ÷ Δtime
速度 = 距离变化量 ÷ 时间变化量
Here, the Greek letter Δ (delta) means 'change in'. So Δdistance means the final distance minus the starting distance.
这里的希腊字母 Δ（delta）表示“变化量”。因此，Δdistance 表示末距离减去起始距离。
4. Calculating Speed from a Graph | 从图像计算速度
To calculate speed from a straight line segment, choose two easy-to-read points on that segment. Then use the formula:
要从一条直线段计算速度，请在该线段上选择两个易于读取的点。然后使用公式：
speed = distance ÷ time
速度 = 距离 ÷ 时间
distance is 120 km, and the change in time is 4 hours, so the speed is 120 ÷ 4 = 30 km/h.
示例：一辆汽车从 (0, 0) 行驶到 (4, 120)。距离变化量为 120 千米，时间变化量为 4 小时，因此速度为 120 ÷ 4 = 30 千米/小时。
If the graph uses metres and seconds, your answer will be in m/s. If it uses kilometres and hours, your answer will be in km/h. Always include the correct unit.
如果图像使用米和秒，答案单位就是米/秒。如果使用千米和小时，答案单位就是千米/小时。务必写出正确单位。
5. Constant Speed and Rest | 匀速与静止
A straight sloping line means the object is moving at a constant speed. The slope does not change, so the speed does not change.
一条倾斜的直线表示物体正在匀速运动。斜率不变，因此速度也不变。
A horizontal line means the distance is not changing while time is still passing. This tells you the object is stationary, or at rest.
水平线表示距离不随时间变化而变化。这告诉你物体处于静止状态，或者说停下来了。
| Line type | 线段类型 | Meaning | 含义 | Speed | 速度 |
|---|---|---|
| Upward sloping straight line | Moving away from start | Constant speed |
| Horizontal line | Stopped / resting | Zero |
| Downward sloping straight line | Returning to start | Constant speed in reverse |
| Curved line | Speed is changing | Not constant |
6. Acceleration and Changing Speed | 加速度与变速
In KS3, you may see a curved line on a distance-time graph. A curved line tells you that the speed is not constant; the object is accelerating or decelerating.
在 KS3 阶段，你可能会在距离-时间图上看到曲线。曲线表示速度不恒定；物体正在加速或减速。
If the curve becomes steeper as time passes, the distance is increasing more quickly, so the object is speeding up. If the curve becomes less steep, the object is slowing down.
如果曲线随时间推移变得越来越陡，说明距离增加得越来越快，物体正在加速。如果曲线变得越来越平缓，说明物体正在减速。
You do not need a separate acceleration formula at KS3, but you should be able to describe what the changing slope means in a real journey.
在 KS3 阶段你不需要单独的加速度公式，但你应该能够描述变化斜率在实际行程中的含义。
7. Drawing a Distance-Time Graph | 绘制距离-时间图
To draw a distance-time graph from a data table, first label the axes with clear scales. The x-axis is time and the y-axis is distance. Then plot each pair of values as a point.
要根据数据表绘制距离-时间图，首先给坐标轴标上清晰刻度。x 轴是时间，y 轴是距离。然后把每一对数值描成点。
If the speed is constant, join the points with a straight line using a ruler. If the object is at rest, draw a horizontal line. Finally, give your graph a title.
如果速度恒定，就用直尺将各点连成直线。如果物体静止，就画水平线。最后给图像加上标题。
Example data: A cyclist travels 10 km in the first hour, rests for the second hour, then travels 20 km in the third hour.
示例数据：一名骑行者第一小时行驶了 10 千米，第二小时休息，第三小时又行驶了 20 千米。
| Time in hours | 时间（小时） | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Distance in km | 距离（千米） | 0 | 10 | 10 | 30 |
The graph would have an upward line from 0 to 1 hour, a horizontal line from 1 to 2 hours, and a steeper upward line from 2 to 3 hours.
该图像会有一条从 0 到 1 小时的上升线，一条从 1 到 2 小时的水平线，以及一条从 2 到 3 小时更陡的上升线。
8. Interpreting Journey Stories | 解读行程故事
Often a question will describe a journey in words and ask you to match it to a graph, or explain what each part of a graph means. Break the journey into stages: moving, stopping, returning and speeding up.
题目经常用文字描述一段行程，然后要求你把它与图像匹配，或者解释图像每一部分的含义。把行程分成几个阶段：移动、停下、返回和加速。
Example: Sarah walks to a shop, stops for ten minutes, then runs home. The graph starts with a shallow upward line, then a horizontal line, then a steep downward line back to the distance zero.
示例：莎拉步行去商店，停了十分钟，然后跑回家。图像先是一条较缓的上升线，接着是水平线，然后是一条较陡的下降线回到距离为零。
The downward slope shows that the distance from the starting point is decreasing. The object is travelling back towards the start.
向下的斜率表示距起点的距离在减少。物体正在返回起点。
9. Common Mistakes | 常见错误
One common mistake is mixing up the axes. Distance always goes on the y-axis, and time always goes on the x-axis. If you swap them, the graph tells a different story.
一个常见错误是混淆坐标轴。距离永远在 y 轴上，时间永远在 x 轴上。如果交换了轴，图像表达的意思就不同了。
Another mistake is thinking that a horizontal line means the object is returning to the start. A horizontal line means the object is staying still, because distance is not changing.
另一个错误是认为水平线表示物体正在返回起点。水平线表示物体保持不动，因为距离没有变化。
Students also sometimes think that a steep line means the ground is steep. In a distance-time graph, a steep line means high speed, not the physical slope of a road or hill.
学生有时还认为陡峭的线意味着路面很陡。在距离-时间图中，陡峭的线表示高速度，而不是现实中的道路或山坡坡度。
Finally, always check whether time is in hours or minutes before calculating speed. If needed, convert units so that distance and time match, such as km with hours or m with seconds.
最后，计算速度前一定要检查时间是以小时还是分钟为单位。如有需要，请换算单位，使距离和时间匹配，例如千米对应小时，或米对应秒。
10. Exam-Style Practice Question | 考试风格练习题
Question: A train leaves a station and travels 60 km in 1 hour. It stops at a station for 30 minutes, then travels another 30 km in 30 minutes. Draw a distance-time graph and calculate the train's average speed for the whole journey in km/h.
题目：一列火车离开车站，1 小时行驶了 60 千米。它在一个车站停了 30 分钟，然后用 30 分钟又行驶了 30 千米。请绘制距离-时间图，并计算火车全程的平均速度，单位用千米/小时。
Use the formula for average speed: average speed = total distance ÷ total time.
使用平均速度公式：平均速度 = 总距离 ÷ 总时间。
- Total distance: 60 km + 30 km = 90 km
- Total time: 1 h + 0.5 h + 0.5 h = 2 h
- Average speed: 90 ÷ 2 = 45 km/h
中文要点：
- 总距离：60 千米 + 30 千米 = 90 千米
- 总时间：1 小时 + 0.5 小时 + 0.5 小时 = 2 小时
- 平均速度：90 ÷ 2 = 45 千米/小时
11. Step-by-Step Solution | 分步解答
Step 1: Draw the axes. Label the x-axis as time in hours from 0 to 2, and the y-axis as distance in km from 0 to 100.
第 1 步：画出坐标轴。将 x 轴标记为时间（小时），从 0 到 2；将 y 轴标记为距离（千米），从 0 到 100。
Step 2: Plot the points for each stage. After 1 hour the distance is 60 km, so plot (1, 60). After 1.5 hours the distance is still 60 km, so plot (1.5, 60). After 2 hours the distance is 90 km, so plot (2, 90).
第 2 步：描出每个阶段的点。1 小时后距离为 60 千米，所以描出 (1, 60)。1.5 小时后距离仍为 60 千米，所以描出 (1.5, 60)。2 小时后距离为 90 千米，所以描出 (2, 90)。
Step 3: Join the points. From (0, 0) to (1, 60) draw a straight line. From (1, 60) to (1.5, 60) draw a horizontal line. From (1.5, 60) to (2, 90) draw another straight line.
第 3 步：连接各点。从 (0, 0) 到 (1, 60) 画一条直线。从 (1, 60) 到 (1.5, 60) 画一条水平线。从 (1.5, 60) 到 (2, 90) 画另一条直线。
and simply divide the total distance by the total time. This gives 90 km ÷ 2 h = 45 km/h.
第 4 步：计算平均速度时，忽略中间停留，直接用总距离除以总时间。得到 90 千米 ÷ 2 小时 = 45 千米/小时。
12. Key Takeaways | 核心要点
A distance-time graph shows a journey on a grid. The x-axis is time, and the y-axis is distance. The slope of the line is the speed.
距离-时间图在网格上展示一段行程。x 轴是时间，y 轴是距离。线段的斜率就是速度。
A steeper line means faster movement. A horizontal line means the object is at rest. A downward line means the object is returning to the start.
线越陡，运动越快。水平线表示物体静止。向下的线表示物体正在返回起点。
Always calculate speed as distance divided by time, and remember to include the correct unit such as m/s or km/h.
计算速度时始终用距离除以时间，并记得写上正确单位，如米/秒或千米/小时。
If the line is curved, the speed is changing. If the line is straight, the speed is constant for that part of the journey.
如果线是曲线，速度在变化。如果线是直线，则在该段行程中速度保持不变。
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