📚 Speed-Time Graphs: Reading and Analysis | 速度-时间图像的读图与分析
A speed-time graph is one of the most powerful tools for describing motion in mathematics. It shows how an object’s speed changes over time, and it allows us to read acceleration and distance directly from the graph.
速度-时间图像是数学中描述运动最有力的工具之一。它展示了物体速度随时间变化的情况，并且让我们能够直接从图像中读出加速度和路程。
1. What Is a Speed-Time Graph? | 什么是速度-时间图像？
A speed-time graph has time on the horizontal axis and speed on the vertical axis. Every point on the graph has coordinates \((t, v)\), meaning that at a particular time \(t\), the object is moving at speed \(v\).
速度-时间图像以时间为横轴，以速度为纵轴。图像上的每个点都有坐标 \((t, v)\)，表示在某个时间 \(t\)，物体的速度是 \(v\)。
It is important to understand that the graph is not a picture of the path the object takes. It only shows how speed changes as time passes.
需要理解的是，速度-时间图像并不是物体运动路径的图画，它只表示速度随时间的变化情况。
2. Axes and Key Features | 坐标轴与关键特征
The horizontal axis is usually measured in seconds, and the vertical axis is usually measured in metres per second. The vertical axis can also be written as m/s.
横轴通常以秒为单位，纵轴通常以米每秒为单位，纵轴单位也可以写为 m/s。
On a speed-time graph, speed is never negative. If the line touches the time axis, the object is stationary at that moment.
在速度-时间图像中，速度永远不会是负数。如果图像与时间轴相交，说明物体在该时刻是静止的。
| Axis / 坐标轴 | Quantity / 物理量 | Unit / 单位 |
| Horizontal / 横轴 | Time / 时间 | second / 秒, s |
| Vertical / 纵轴 | Speed / 速度 | metre per second / 米每秒, m/s |
To read a graph correctly, treat it like a set of coordinates. Find a time on the horizontal axis, then read the corresponding speed on the vertical axis.
要正确读图，可以把图像看作一组坐标。先在横轴上找到时间，再在纵轴上读出对应的速度。
3. Reading Values from the Graph | 从图像读取数值
To find the speed at a given time, draw an imaginary vertical line from that time value up to the graph, then read the speed from the vertical axis.
要找到某个时刻的速度，可以在横轴上找到对应的时间，沿竖直方向向上作辅助线到达图像，再从纵轴读出速度。
To find the time at which an object has a particular speed, draw a horizontal line from that speed value until it meets the graph, then read the time from the horizontal axis.
要找到物体达到某一速度的时间，可以在纵轴上找到该速度，沿水平方向作辅助线直到与图像相交，再从横轴读出时间。
For example, if the graph passes through the point \((5, 20)\), then after 5 seconds the object is moving at 20 m/s. If the graph crosses 15 m/s at \(t = 3\), then the object reaches 15 m/s after 3 seconds.
例如，如果图像经过点 \((5, 20)\)，那么在第 5 秒时，物体的速度为 20 m/s。如果图像在 \(t = 3\) 时达到 15 m/s，那么物体在第 3 秒时速度达到 15 m/s。
4. Gradient Means Acceleration | 斜率表示加速度
For a straight-line section of a speed-time graph, the gradient is the acceleration. The steeper the line, the greater the acceleration.
对于速度-时间图像中的直线段，斜率就是加速度。直线越陡，加速度越大。
acceleration = gradient = Δv / Δt = (v – u) / t
Here, \(u\) is the initial speed, \(v\) is the final speed, and \(t\) is the time interval. The symbol \(\Delta\) means “change in”.
其中，\(u\) 是初速度，\(v\) 是末速度，\(t\) 是时间间隔。符号 \(\Delta\) 表示“变化量”。
If the gradient is positive, the object is speeding up. If the gradient is negative, the object is slowing down. If the gradient is zero, the object is moving at constant speed.
如果斜率为正，物体在加速。如果斜率为负，物体在减速。如果斜率为零，物体在做匀速运动。
For example, if speed changes from 0 m/s to 20 m/s in 4 seconds, then the acceleration is \(20 \div 4 = 5\) m/s².
例如，如果速度在 4 秒内从 0 m/s 变为 20 m/s，那么加速度就是 \(20 \div 4 = 5\) m/s²。
5. Area Means Distance | 面积表示路程
The area between the graph and the time axis represents the total distance travelled by the object.
图像与时间轴之间的面积，表示物体运动的总路程。
distance = area under the speed-time graph
The unit of this area is the unit of speed multiplied by the unit of time. Since speed is measured in m/s and time is measured in s, the area has units of metres.
面积的单位等于速度单位乘以时间单位。由于速度以 m/s 为单位，时间以秒为单位，因此面积的单位是米。
For simple shapes, use area formulas. For a triangle, the area is \(\frac{1}{2} \times \text{base} \times \text{height}\). For a trapezium, the area is \(\frac{1}{2} \times (a + b) \times h\).
对简单图形，可以使用面积公式。三角形的面积是 \(\frac{1}{2} \times 底 \times 高\)。梯形的面积是 \(\frac{1}{2} \times (上底 + 下底) \times 高\)。
If the graph is curved, the area can be estimated by counting squares or by splitting the shape into strips.
如果图像是曲线，可以通过数方格或把图形分成若干小条来估算面积。
6. Interpreting Different Shapes | 常见图像形状的解读
-
A horizontal line above the time axis means the object is moving at constant speed, with zero acceleration.
时间轴上方的水平线表示物体做匀速运动，加速度为零。
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A straight line rising from left to right means uniform acceleration: the speed increases at a steady rate.
从左向右上升的直线表示匀加速运动：速度均匀增加。
-
A straight line falling from left to right means uniform deceleration: the speed decreases at a steady rate.
从左向右下降的直线表示匀减速运动：速度均匀减小。
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A curved line means acceleration is changing. The curve gets steeper when acceleration increases, and less steep when acceleration decreases.
曲线表示加速度在变化。曲线变陡说明加速度增大，曲线变缓说明加速度减小。
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A horizontal line exactly on the time axis means the object is stationary.
正好落在时间轴上的水平线表示物体静止不动。
7. Worked Example | 例题分析
A car starts from rest, accelerates uniformly for 8 seconds to 20 m/s, travels at 20 m/s for 12 seconds, and then brakes uniformly to rest in 4 seconds. Find the total distance and the average speed.
一辆汽车从静止开始启动，用 8 秒均匀加速到 20 m/s，然后以 20 m/s 匀速行驶 12 秒，最后用 4 秒均匀减速直到停止。求总路程和平均速度。
| Section / 阶段 | Time / 时间 | Shape
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