KS3 Maths: Kinematics Key Points | KS3 数学：运动学考点精讲

📚 KS3 Maths: Kinematics Key Points | KS3 数学：运动学考点精讲

Kinematics is the branch of mathematics that describes motion. At KS3 level, you learn to calculate speed, distance, and time using simple formulas, interpret distance‑time graphs, and convert between common units of speed. Mastering these fundamentals will give you confidence when you later encounter more advanced topics like acceleration in GCSE Physics and Maths.

运动学是描述运动的数学分支。在 KS3 阶段，你会学习如何使用简单的公式计算速度、距离和时间，解读距离‑时间图，以及转换常见的速度单位。掌握这些基础知识会让你以后在 GCSE 物理和数学中遇到加速度等更高级主题时充满信心。

1. What is Kinematics? | 什么是运动学？

Kinematics focuses on how objects move, without worrying about the forces that cause the motion. You will work with quantities such as distance, time, speed, and later velocity and acceleration. For KS3 maths, the emphasis is on uniform (steady) motion and understanding the relationship between distance, speed, and time.

运动学关注物体如何运动，而不考虑导致运动的力。你会接触路程、时间、速度等量，将来还会学习速率和加速度。在 KS3 数学中，重点在于匀速运动以及理解距离、速度和时间之间的关系。

2. Speed, Distance, and Time Basics | 速度、距离和时间基础

Speed tells you how fast an object is moving. Distance is how far the object travels. Time is the duration of the journey. These three are linked by a very important equation. If you know any two of them, you can work out the third.

速度告诉你物体运动有多快。距离是物体移动的路程。时间是行程的持续时长。这三者由一个非常重要的公式联系起来。如果你知道其中任意两个量，就可以求出第三个。

3. The Speed Formula | 速度公式

The formula that connects speed, distance, and time is:

Speed = Distance ÷ Time

Some people remember this as the triangle: put D on top, and S and T on the bottom. Cover the quantity you want to leave the correct calculation.

连接速度、距离和时间的公式为：

速度 = 距离 ÷ 时间

有些人用三角形记忆法：把 D 放在顶部，S 和 T 放在底部。盖住你要求的量，剩下的就是正确的计算公式。

4. Rearranging the Formula | 公式变形

You must be able to rearrange the speed formula. To find distance, use:

Distance = Speed × Time

To find time, use:

Time = Distance ÷ Speed

Practise switching between these forms until it becomes automatic.

你必须能够对速度公式进行变形。要求距离，用：

距离 = 速度 × 时间

要求时间，用：

时间 = 距离 ÷ 速度

练习在这些形式之间切换，直至能够自动反应。

5. Units of Speed | 速度的单位

Speed can be measured in metres per second (m/s) or kilometres per hour (km/h). In KS3 maths, you will often see both. Always check the units given in a problem and make sure your answer uses the correct ones. Sometimes you may need to convert distances or times first (e.g. minutes to hours).

速度可以用米每秒 (m/s) 或千米每小时 (km/h) 来衡量。在 KS3 数学中，你经常会见到这两种单位。始终检查题目给出的单位，确保你的答案使用正确的单位。有时你需要先转换距离或时间（例如把分钟转化为小时）。

6. Converting Units: m/s to km/h | 单位转换：米每秒与千米每小时

To change m/s to km/h, multiply by 3.6. This is because 1 m/s means 3600 metres per hour, which is 3.6 km/h. To change km/h to m/s, divide by 3.6.

将米每秒转化为千米每小时，乘以 3.6。这是因为 1 m/s 意味着每小时 3600 米，也就是 3.6 km/h。将千米每小时转化为米每秒，则除以 3.6。

From m/s to km/h	× 3.6
From km/h to m/s	÷ 3.6

7. Average Speed | 平均速度

In real life, objects don’t always move at a constant speed. Average speed is the total distance travelled divided by the total time taken. Even if a car speeds up and slows down, the average speed tells you the overall rate of the whole journey.

在现实生活中，物体并不总是以恒定速度运动。平均速度是总路程除以总时间。即使一辆汽车忽快忽慢，平均速度也能告诉你整个行程的整体快慢程度。

Example: A cyclist covers 15 km in 0.75 hours. Average speed = 15 ÷ 0.75 = 20 km/h.

例子：一位骑行者 0.75 小时行驶了 15 千米。平均速度 = 15 ÷ 0.75 = 20 km/h。

8. Distance-Time Graphs | 距离‑时间图

A distance‑time graph shows how distance from a starting point changes over time. Time is on the horizontal axis (x‑axis) and distance is on the vertical axis (y‑axis). These graphs are very useful for visualising motion.

距离‑时间图显示从起点出发的距离如何随时间变化。时间在横轴（x 轴）上，距离在纵轴（y 轴）上。这些图对于直观显示运动非常有用。

A straight line sloping upwards means constant speed.
A horizontal line means the object is at rest (stationary).
A steeper line means a greater speed.

一条向上倾斜的直线表示匀速运动。
一条水平线表示物体静止。
线条越陡，速度越大。

9. Interpreting Graphs: Steady Speed and Rest | 图线解读：匀速与静止

When the line is straight and diagonal, the gradient (slope) equals the speed. To calculate speed from a distance‑time graph, pick two points on the straight line and find the change in distance (vertical) divided by the change in time (horizontal).

当图线是一条笔直的斜线时，其梯度（斜率）等于速度。要从距离‑时间图计算速度，在直线上取两个点，用距离的变化（纵向）除以时间的变化（横向）。

Speed = (distance₂ – distance₁) ÷ (time₂ – time₁)

速度 = (距离₂ – 距离₁) ÷ (时间₂ – 时间₁)

A curved line indicates changing speed (acceleration or deceleration), but at KS3 you will often focus on straight‑line segments.

曲线表示速度在变化（加速或减速），但在 KS3 阶段，你通常只需要处理直线段。

10. Solving Problems with Distance‑Time Graphs | 利用距离‑时间图解题

You may be asked to draw a distance‑time graph from a description of a journey, or to describe a journey from a given graph. Practise turning worded problems into a table of time and distance values, plot the points, and join them with straight lines where appropriate.

你可能会被要求根据行程描述绘制距离‑时间图，或者根据给定的图描述行程。请练习将文字问题转化为时间和距离的数值表格，描点，并在适当位置用直线连接。

Example: ‘A car travels at a steady speed for 2 hours covering 100 km, then stops for a 1‑hour rest, then continues for another 3 hours covering 150 km.’ Draw the graph as three line segments: one sloping up, one horizontal, then another sloping up.

例子：“一辆车以恒定速度行驶了 2 小时，行程 100 千米，然后停下休息 1 小时，再继续行驶 3 小时，行程 150 千米。” 将图画为三条线段：一段向上倾斜，一段水平，然后另一段向上倾斜。

11. Common Mistakes | 常见错误

Confusing minutes with hours: always convert time into hours if speed is in km/h, or into seconds if speed is in m/s.
Forgetting to use average speed when the journey has different parts.
Mixing up the axes on a distance‑time graph – remember, time always goes on the x‑axis.
Using the total distance for a line segment’s speed instead of the distance covered in that segment.

混淆分钟与小时：如果速度单位是 km/h，总要把时间转换为小时；如果是 m/s 则转换为秒。
忘记了当行程包含不同阶段时应该使用平均速度。
在距离‑时间图上混淆坐标轴——记住，时间始终在 x 轴上。
用总距离代替某一段线段的速度计算时应使用该段内经过的距离。

12. Practice Tips | 练习建议

To become confident with kinematics at KS3, work through plenty of examples that combine unit conversion, speed calculations, and graph interpretation. Set yourself challenges like drawing a distance‑time graph of your journey to school.

要在 KS3 阶段掌握运动学，请大量练习包含单位转换、速度计算和图线解读的例题。给自己一点挑战，比如画一张你上学路程的距离‑时间图。

Also, use the triangle method to check your rearranged formulas quickly, and always write down your working step by step, including units at each stage.

此外，用三角形方法快速核验你的公式变形，并始终一步步写下你的解题过程，每一步都要带上单位。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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KS3 Maths: Kinematics Key Points | KS3 数学：运动学考点精讲