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Graphs and Kinematics: Teacher's Book 400 Revision Notes | 图像与运动学：教师用书 400 复习笔记

2026-08-21 18:50 · 本文部分内容由AI辅助创作

📚 Graphs and Kinematics: Teacher's Book 400 Revision Notes | 图像与运动学：教师用书 400 复习笔记

In IGCSE Mathematics, distance-time and speed-time graphs regularly appear in both Core and Extended papers. This revision note follows the Teacher's Book 400 approach to help you interpret gradients, areas and real motion accurately.

在 IGCSE 数学中，距离-时间图和速度-时间图经常出现在核心卷和扩展卷中。本篇复习笔记按照教师用书 400 的思路，帮助你准确解读斜率、面积和真实运动。

1. Why Kinematics Graphs Matter | 为什么运动学图像重要

Kinematics graphs link algebra, geometry and real-world motion in one topic. Exam questions often ask you to find speed from a distance-time graph or distance from a speed-time graph.

运动学图像将代数、几何和现实运动结合在一个主题中。考试题目经常要求你从距离-时间图求速度，或从速度-时间图求距离。

The key skills are reading axes, calculating gradients and finding areas under straight-line sections. These are transferable skills that also appear in other graph-based questions.

关键技能是读取坐标轴、计算斜率和求直线段下方区域的面积。这些是可迁移的技能，也会出现在其他图像类题目中。

2. Distance-Time Graphs: The Basics | 距离-时间图基础

In a distance-time graph, time is plotted on the horizontal axis and total distance from the starting point is plotted on the vertical axis.

在距离-时间图中，时间绘制在横轴上，从起点开始计算的总距离绘制在纵轴上。

A straight, upward-sloping line represents constant speed. A horizontal line means the object is stationary because the distance does not change as time increases.

一条向上倾斜的直线表示恒定速度。水平线表示物体静止，因为距离不随时间的增加而改变。

The gradient of a distance-time graph gives the speed. The steeper the line, the greater the speed.

距离-时间图的斜率表示速度。直线越陡，速度越大。

speed = Δdistance ÷ Δtime

3. Finding Speed from a Distance-Time Graph | 从距离-时间图求速度

To find speed, choose two points on a straight section of the graph. Find the change in distance and the change in time between those two points.

要求速度，请在图像的直线段上选择两个点。找到这两点之间距离的变化量和时间的变化量。

m in 4 s, then speed = 80 ÷ 4 = 20 m/s. Always state the correct unit such as m/s or km/h.

例如，如果一辆车在 4 s 内行驶了 80 m，那么速度 = 80 ÷ 4 = 20 m/s。始终注明正确单位，如 m/s 或 km/h。

If the graph uses kilometres and hours, the speed will be in km/h. Do not mix units within the same calculation.

如果图像使用千米和小时，速度单位就是 km/h。不要在同一次计算中混用单位。

4. Speed-Time Graphs: The Basics | 速度-时间图基础

In a speed-time graph, time is on the horizontal axis and speed is on the vertical axis. A horizontal line on a speed-time graph means the object is moving at constant speed.

在速度-时间图中，横轴表示时间，纵轴表示速度。速度-时间图上的水平线表示物体以恒定速度运动。

An upward-sloping straight line means the object is accelerating. A downward-sloping straight line means the object is decelerating, or slowing down.

向上倾斜的直线表示物体在加速。向下倾斜的直线表示物体在减速，即速度变慢。

On a speed-time graph, the gradient gives the acceleration. This is different from a distance-time graph, where the gradient gives speed.

在速度-时间图中，斜率表示加速度。这与距离-时间图不同，后者的斜率表示速度。

5. Acceleration as the Gradient | 加速度作为斜率

Acceleration is the rate of change of speed. It can be calculated by dividing the change in speed by the time taken for that change.

加速度是速度变化的快慢。可以通过速度变化量除以变化所需的时间来计算。

a = Δv ÷ Δt

if a cyclist changes speed from 12 m/s to 20 m/s in 8 s, then a = (20 − 12) ÷ 8 = 1 m/s².

例如，如果一名骑行者速度从 12 m/s 变为 20 m/s，用时 8 s，那么 a = (20 − 12) ÷ 8 = 1 m/s²。

Negative acceleration, or deceleration, is found when the final speed is less than the initial speed. The unit for acceleration is m/s².

当末速度小于初速度时，得到负加速度，即减速度。加速度的单位是 m/s²。

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6. Distance as the Area Under a Speed-Time Graph | 速度-时间图下面积求距离

The area under a speed-time graph represents the distance travelled. You can often split the area into rectangles and triangles to make the calculation easier.

速度-时间图下方的面积表示行驶距离。你通常可以把该面积拆分成矩形和三角形，以便计算。

section, use area = speed × time. For a triangular section, use area = ½ × base × height.

对于矩形部分，使用面积 = 速度 × 时间。对于三角形部分，使用面积 = ½ × 底 × 高。

area = ½ × (a + b) × h, where a and b are the parallel speeds and h is the time interval.

如果某部分是梯形，使用面积 = ½ × (a + b) × h，其中 a 和 b 是两条平行边对应的速度，h 是时间间隔。

Always add the areas of all sections to find the total distance travelled.

始终将所有部分的面积相加，才能得到总行驶距离。

7. Comparing the Two Graph Types | 距离-时间图与速度-时间图对比

Students often confuse the two graph types. The table below summarises what the gradient, area and horizontal line mean in each case.

学生经常混淆这两种图像。下表总结了在每种图像中斜率、面积和水平线的含义。

Feature / 特征 Distance-time graph / 距离-时间图 Speed-time graph / 速度-时间图
Gradient / 斜率 Speed / 速度 Acceleration / 加速度
Area under graph / 图像下面积 No direct physical meaning / 无直接物理意义 Distance travelled / 行驶距离
Horizontal line / 水平线 Stationary / 静止 Constant speed / 恒定速度

When you read a question, underline whether it says distance-time or speed-time before starting any calculation.

阅读题目时，请先划出它说的是距离-时间图还是速度-时间图，再开始计算。

8. Common Misconceptions | 常见误区