📚 Kinematics Graphs: Distance-Time and Speed-Time Graphs | 运动学图像解读：距离-时间图与速度-时间图
In IGCSE mathematics, travel graphs are used to model motion in a visual way. A distance-time graph shows how far an object has moved from a starting point, while a speed-time graph shows how its speed changes. Understanding gradients and areas on these graphs is a core skill for both calculator and non-calculator papers.
在 IGCSE 数学中，行程图用于直观地表示运动。距离-时间图显示物体从起点移动了多远，而速度-时间图显示速度如何变化。理解这些图像上的斜率和面积是计算器卷和非计算器卷中的核心技能。
1. Variables and Axes | 变量与坐标轴
Time is always plotted on the horizontal x-axis, and the quantity measuring motion is plotted on the vertical y-axis. For a distance-time graph, the vertical axis is distance from a fixed point, usually in metres or kilometres. For a speed-time graph, the vertical axis is speed, usually in metres per second or kilometres per hour.
时间总是标在水平 x 轴上，用于衡量运动的量标在竖直 y 轴上。对于距离-时间图，纵轴表示距离起点的距离，通常以米或千米为单位。对于速度-时间图，纵轴表示速度，通常以米每秒或千米每小时为单位。
Always label axes with both the quantity and the unit, for example 'time (s)' and 'distance (m)'. If the graph has no labels, you cannot assume the scale or the meaning of the gradient.
坐标轴必须同时标出物理量和单位，例如 "时间 (s)" 和 "距离 (m)"。如果图像没有标注，就不能假设刻度和斜率的含义。
2. Distance-Time Graphs: Gradient as Speed | 距离-时间图：斜率表示速度
On a distance-time graph, the gradient between two points measures speed. A steeper line means a higher speed, because the same time produces a larger change in distance.
在距离-时间图上，两点之间的斜率表示速度。线越陡，速度越大，因为相同时间内距离变化更大。
speed = change in distance ÷ change in time = Δd ÷ Δt
A straight diagonal line represents constant speed. A horizontal line means the object is stationary, because distance does not change as time increases.
一条斜直线表示匀速运动。水平线表示物体静止，因为距离不随时间变化。
3. Reading Stationary and Constant-Speed Sections | 识别静止与匀速段
When a distance-time graph has several straight segments, each segment tells a separate part of the journey. A flat segment means the object has stopped. A positive gradient means moving away from the start; a negative gradient in a displacement-time graph would mean moving back toward the starting point.
当距离-时间图由多条直线段组成时，每一段描述行程的不同部分。水平段表示物体停下来。正斜率表示远离起点；在位移-时间图中，负斜率表示返回起点。
In IGCSE questions, distance is usually total distance rather than displacement, so the graph never goes downwards; it can only stay flat or rise. If a graph does fall, it is likely a displacement-time graph, and you should interpret negative gradient as movement in the opposite direction.
在 IGCSE 题目中，距离通常是总路程而非位移，因此图像不会下降，只会保持水平或上升。如果图像下降，很可能是位移-时间图，此时负斜率应理解为向相反方向运动。
| Distance-time graph feature (图像特征) | Meaning (含义) |
| Horizontal line (水平线) | Stationary (静止) |
| Straight sloping line (斜直线) | Constant speed (匀速) |
| Steeper slope (更陡的斜率) | Higher speed (更高的速度) |
| Curved line becoming steeper (越来越陡的曲线) | Speeding up (加速) |
4. Instantaneous Speed from a Curved Distance-Time Graph | 从曲线距离-时间
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