📚 Distance-Time Graphs | 距离-时间图
A distance-time graph shows how far an object has travelled over a period of time. It is a powerful visual tool for understanding motion, speed, and even stationary periods. By interpreting the slope and shape of the graph, you can describe exactly what is happening at each stage of a journey.
距离-时间图展示的是物体在一段时间内移动了多远。它是理解运动、速度甚至静止时段的强大可视化工具。通过解读图形的斜率和形状，你可以准确描述旅程中每个阶段发生的情况。
1. The Axes and What They Mean | 坐标轴及其含义
The horizontal axis (x-axis) always represents time. Time usually increases from left to right, and units can be seconds, minutes, or hours. The vertical axis (y-axis) represents distance from a starting point, measured in metres, kilometres, or miles.
横轴（x 轴）始终表示时间。时间通常从左向右递增，单位可以是秒、分钟或小时。纵轴（y 轴）表示距起点的距离，以米、公里或英里为单位。
A point on the graph tells you the object’s distance from home at a particular time. If the point lies on the horizontal axis, the distance is zero – the object is at the starting position.
图上的一个点告诉你物体在特定时刻离原点的距离。如果点位于横轴上，则距离为零——物体在起始位置。
- Always label axes clearly and include units.
- 始终清晰地标注坐标轴并标明单位。
2. What a Straight Sloping Line Means | 直线倾斜段的含义
A straight line sloping upwards from left to right indicates constant speed. The object covers equal distances in equal time intervals. The steeper the line, the faster the object is moving.
从左向右向上倾斜的直线表示匀速运动。物体在相等的时间间隔内行驶相等的距离。直线越陡，物体移动速度越快。
If the line tilts downwards, the object is returning towards the starting point, still at a constant speed. Distance decreases over time.
如果线条向下倾斜，表示物体正在返回起点，同样保持恒定速度。距离随时间减少。
To calculate the speed from a straight distance-time graph, use the formula:
要从直线的距离-时间图计算速度，使用以下公式：
speed = distance ÷ time
3. Horizontal Lines and Stationary Objects | 水平线与静止物体
A flat horizontal line means the object is not moving – its distance does not change as time passes. This could represent a rest break, waiting at traffic lights, or a pause in a journey.
一条平坦的水平线表示物体静止不动——随着时间的推移，距离没有变化。这可能代表休息、在红绿灯处等待或旅程中的停顿。
The length of the horizontal segment shows the duration of the stop. Even though the object is stationary, time continues to elapse.
水平线段的长度显示了停顿时长。即使物体静止不动，时间仍在流逝。
4. Curved Lines and Changing Speed | 曲线与速度变化
A curved line means the speed is changing – the object is accelerating or decelerating. If the curve becomes steeper over time, the object is speeding up.
曲线表示速度正在变化——物体在加速或减速。如果曲线随时间变得越来越陡，物体正在加速。
If the curve flattens out, the object is slowing down. A curve that eventually becomes horizontal shows the object coming to a stop.
如果曲线逐渐变平，物体在减速。最终变为水平的曲线表示物体停了下来。
5. Calculating Speed from a Graph | 从图上计算速度
To find speed between two points on a distance-time graph, pick two points and calculate the rise (change in distance) and the run (change in time). Then divide the rise by the run.
要在距离-时间图上求两点之间的速度，选择两个点，计算高度变化（距离变化）和水平变化（时间变化），然后用高度变化除以水平变化。
speed = (distance₂ − distance₁) ÷ (time₂ − time₁)
If the graph is not a single straight line, the speed found this way is the average speed over the chosen time interval. For curved sections, speed is changing continuously.
如果图形不是一条直线，用这种方法求得的是所选时间间隔内的平均速度。对于曲线部分，速度在不断变化。
6. Describing a Journey in Sections | 分段描述旅程
A complete journey graph is often made up of several line segments. You can describe each segment separately: e.g., ‘First, the cyclist rode at a steady speed away from home for 10 minutes, then stopped for a 5-minute rest, then rode back home more slowly.’
一张完整的行程图通常由几条线段组成。你可以分别描述每一段：例如，“骑行者先以恒定速度离家骑行了10分钟，然后休息了5分钟，再以较慢的速度骑回家。”
You can also estimate total distance travelled by adding the lengths of all upward and downward segments, but remember that downward segments still represent movement – just in the opposite direction.
你也可以通过把所有上升段和下降段的距离相加来估算总行程距离，但要记住下降段也表示运动——只是方向相反。
7. Common Units and Conversions | 常见单位及换算
Graphs may use mixed units. If distance is in km and time in hours, speed is in km/h. If distance is in m and time in seconds, speed is in m/s. You might need to convert between units.
图表可能使用混合单位。如果距离单位是公里、时间单位是小时，速度单位就是公里/小时。如果距离单位是米、时间单位是秒，速度单位就是米/秒。你可能需要进行单位换算。
- 1 hour = 60 minutes = 3600 seconds
- 1 小时 = 60 分钟 = 3600 秒
- 1 km = 1000 m
- 1 公里 = 1000 米
When reading values from a graph, always check the scale on both axes before calculating speed. A common mistake is misreading sub-divisions on the axes.
从图上读取数值时，在计算速度前务必检查两轴的刻度。一个常见错误是误读轴上的小格。
8. Drawing a Distance-Time Graph | 绘制距离-时间图
To draw a graph from a description, first create a table of times and corresponding distances. Then plot the points on a grid, using a sharp pencil and ruler for straight lines, and a smooth curve for changing speeds.
要根据文字描述绘制图形，首先制作一个时间与对应距离的表格。然后在网格上描点，用尖铅笔和直尺画直线段，用平滑曲线表示变速运动。
Label the axes with the correct units and give the graph a title. Check that the points follow the story: do not join points with a straight line if the motion is supposed to involve stops or changes in speed.
用正确的单位标注坐标轴，并给图表加上标题。检查这些点是否符合故事：如果运动过程中有停顿或速度变化，不要用直线连接这些点。
9. Interpreting the Starting Point | 理解起点
Not all journeys begin at zero distance. A graph may start at a positive distance on the y-axis if the object is already some distance away from the reference point at time zero.
并非所有行程都从距离零开始。如果物体在时间为零时已经距离参考点有一段距离，图形可能在 y 轴的正距离处开始。
Similarly, the graph may end at a distance greater than zero if the object has not returned home. Always read the context carefully.
同样，如果物体没有返回出发点，图形可能以大于零的距离结束。一定要仔细阅读上下文。
10. Comparing Two Objects on the Same Graph | 在同一张图上比较两个物体
You can show two journeys on the same axes using different colours or line styles. The steeper line indicates the higher speed. Where the lines cross, the two objects are at the same distance at the same time – they meet.
你可以用不同颜色或线条样式在同一坐标轴上表示两段行程。较陡的线表示较高的速度。两条线相交时，两物体在相同时间位于相同距离处——它们相遇了。
If a line is above another, that object is further ahead. Using the graph, you can determine who arrived first, when overtaking occurred, and how long each waited.
如果一条线在另一条线上方，则该物体领先得更远。通过图表，你可以判断谁先到达、超车发生在何时，以及各自等待了多久。
11. Common Misconceptions | 常见误解
- Misconception: A steep downward line means the object is decelerating. Reality: It means it is returning at a high constant speed. The steepness indicates the magnitude of speed, not whether speed is increasing or decreasing.
- 误解： 陡峭的下降线表示物体在减速。事实： 它表示物体正以较高的恒定速度返回。陡峭程度表示速度的大小，而不是速度的增减。
- Misconception: A flat line means time has stopped. Reality: Time always moves forward; the object is simply not changing its distance.
- 误解： 平坦的线表示时间停止了。事实： 时间一直在前进；只是物体的距离没有变化。
12. Practice Problem Walkthrough | 典型例题演练
Example problem: A graph shows a cyclist leaves home at 08:00, rides 12 km in 40 minutes, rests for 20 minutes, and returns home in 30 minutes. Plot the journey and find the speed for the outward leg.
例题： 图表显示一名骑行者早上8点离家，40分钟骑行了12公里，休息20分钟，再用30分钟返回家中。请画出这段行程图，并计算去程的速度。
| Stage | Time (min) | Distance (km) |
|---|---|---|
| Outward ride | 0–40 | 0 → 12 |
| Rest | 40–60 | 12 (constant) |
| Return ride | 60–90 | 12 → 0 |
Outward speed calculation: distance = 12 km, time = 40 min = ⅔ hour → speed = 12 ÷ (⅔) = 18 km/h. On the graph, the first line would rise steadily to (40, 12), then stay flat to (60, 12), then fall to (90, 0).
去程速度计算：距离 = 12 公里，时间 = 40 分钟 = ⅔ 小时 → 速度 = 12 ÷ (⅔) = 18 公里/小时。在图上，第一条线平稳上升至 (40, 12)，然后持平至 (60, 12)，再下降至 (90, 0)。
By working through such steps, you build confidence in reading and drawing distance-time graphs for any KS3 Cambridge Mathematics problem.
通过练习这样的步骤，你能在解决任何 KS3 剑桥数学距离-时间图问题时建立自信。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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