A-Level Physics: Interpreting Displacement-Time Graphs | A-Level 物理：位移-时间图像解读

📚 A-Level Physics: Interpreting Displacement-Time Graphs | A-Level 物理：位移-时间图像解读

Displacement-time graphs are one of the most essential visual tools in A-Level Physics for describing motion. They show how an object’s position changes relative to a fixed origin over time, and they allow us to read velocities, identify stationary phases, and detect acceleration or deceleration directly from the shape of the graph.

位移-时间图像是 A-Level 物理中描述运动的最重要可视化工具之一。它展示物体相对于固定原点的位置如何随时间变化，使我们能够直接从图像形状读出速度、识别静止阶段，并判断物体是在加速还是减速。

1. What Is a Displacement-Time Graph? | 什么是位移-时间图像？

A displacement-time (s-t) graph plots displacement on the vertical axis (y-axis) and time on the horizontal axis (x-axis). Each point on the graph tells us the position of the object, s, at a particular instant, t. The graph does not show the actual path taken; it only shows the straight-line displacement from the origin.

位移-时间（s-t）图像将位移标在纵轴（y 轴）上，将时间标在横轴（x 轴）上。图像上的每一个点都告诉我们物体在某一时刻 t 的位置 s。图像并不展示物体实际经过的路径，只展示相对于原点的直线位移。

Because displacement is a vector, the values on the y-axis can be positive (on one side of the origin) or negative (on the other side). A point above the time axis means the object is on the positive side of the origin; a point below the time axis means it is on the negative side.

由于位移是矢量，y 轴上的值可以为正（在原点一侧），也可以为负（在原点另一侧）。时间轴上方的点表示物体位于原点正方向一侧；时间轴下方的点表示物体位于原点负方向一侧。

2. Displacement vs Distance | 位移与距离的区别

Distance is a scalar quantity that measures the total length of the path travelled. Direction is not considered. Displacement, on the other hand, is a vector quantity that measures the straight-line change in position from the starting point to the finishing point, including direction.

距离是标量，度量运动路径的总长度，不考虑方向。而位移是矢量，度量从起点到终点的直线位置变化，并包含方向信息。

For example, if a student walks 30 m north and then 30 m south, the total distance travelled is 60 m, but the final displacement is 0 m. On an s-t graph, only displacement is plotted on the y-axis; the graph never records the total path length directly.

例如，如果一个学生先向北走 30 m，再向南走 30 m，他走过的总距离是 60 m，但最终位移是 0 m。在 s-t 图像中，y 轴只标绘位移，图像从不直接记录总路径长度。

3. Gradient Equals Velocity | 梯度等于速度

For any straight-line segment on an s-t graph, the gradient is constant. This gradient gives the velocity of the object:

对于 s-t 图像上的任意直线段，梯度是恒定的。该梯度给出物体的速度：

v = (s₂ − s₁) / (t₂ − t₁) = Δs / Δt

A steeper straight line means a larger speed; a shallower straight line means a smaller speed. The SI unit of velocity is metres per second (m/s), so the gradient must always be calculated as change in displacement (m) divided by change in time (s).

直线越陡，表示速率越大；直线越平缓，表示速率越小。速度的 SI 单位是米每秒（m/s），因此计算梯度时始终要用位移变化量（m）除以时间变化量（s）。

This relationship is one of the most frequently tested ideas in CIE AS Physics. When you see a straight line on an s-t graph, immediately read its gradient as the velocity.

这一关系是 CIE AS 物理中最高频的考点之一。当你在 s-t 图像上看到一条直线时，应立即将它的梯度解读为速度。

4. Horizontal Lines: Stationary Objects | 水平线：静止物体

If a section of the s-t graph is horizontal, parallel to the time axis, then the displacement is not changing. The object is at rest. The gradient is zero, so the velocity is zero.

如果 s-t 图像的某一段是水平的，即平行于时间轴，说明位移不随时间变化，物体处于静止状态。此时梯度为零，速度为零。

A horizontal line does not mean the object is at the origin. It only means the object is not moving from its current position. For example, a car stopped at a traffic light 50 m from the origin would appear as a horizontal line at s = 50 m.

水平线并不表示物体位于原点。它只表示物体没有离开当前位置。例如，一辆停在距原点 50 m 处红绿灯前的汽车，在图像上表现为 s = 50 m 处的水平线。

5. Negative Gradients: Reversing Direction | 负梯度：反向运动

A straight line sloping downwards from left to right has a negative gradient, which means the velocity is negative. The object is moving in the negative direction, usually back towards the origin or beyond it. The magnitude of the gradient still gives the speed.

从左向右向下倾斜的直线具有负梯度，表示速度为负。物体沿负方向运动，通常是返回原点或继续越过原点。梯度的大小仍然表示速率。

If the line crosses the time axis (s = 0), the object is passing through the origin at that instant. After crossing, the displacement becomes negative, meaning the object is on the opposite side of the origin.

如果直线穿过时间轴（s = 0），则物体在该时刻经过原点。穿过之后，位移变为负值，说明物体位于原点的另一侧。

It is important to recognise that a negative velocity does not mean “slowing down”. Slowing down is a decrease in speed, which is the magnitude of velocity. A negative constant velocity simply means constant motion in the opposite direction.

需要特别注意的是，速度为负并不表示”减速”。减速是速率的减小，即速度的大小减小。负的恒定速度仅仅表示沿相反方向做匀速运动。

6. Curved Graphs: Changing Velocity | 曲线：速度变化

When the s-t graph is curved, the gradient changes from point to point, so the velocity is changing. The object is accelerating or decelerating.

当 s-t 图像是曲线时，梯度逐点变化，因此速度也在变化，物体正在加速或减速。

If the curve becomes steeper as time increases, the speed is increasing. If the curve becomes flatter as time increases, the speed is decreasing. Equivalently, look at the direction of the curve’s “bend”: bending upwards to be more vertical means speeding up; bending towards the horizontal means slowing down.

如果曲线随时间变得越来越陡，说明速率增大；如果曲线随时间变得越来越平缓，说明速率减小。等价地，观察曲线的”弯曲”方向：弯向更垂直的方向表示加速；弯向水平方向表示减速。

A special case is a graph that curves downwards while still having a positive gradient. The object is still moving away from the origin, but its speed is decreasing. It will eventually stop if the gradient reaches zero, then it may begin moving back.

一个特殊情况是：曲线虽然向下弯曲，但梯度仍为正值。此时物体仍在远离原点，但速率在减小。如果梯度减小到零，物体最终会停下来，之后可能开始返回。

7. Instantaneous Velocity and Tangents | 瞬时速度与切线

For a curved graph, the gradient at one particular instant is found by drawing a tangent to the curve at that point. The gradient of this tangent is the instantaneous velocity:

对于曲线，某一时刻的梯度需要在该点作切线来求得。切线的梯度即为瞬时速度：

v = Δs / Δt as Δt → 0

In practice, you draw the tangent as a straight line that just touches the curve at the chosen point, then choose two well-separated points on the tangent to calculate its gradient. Choosing points far apart on the tangent improves the accuracy of the reading.

实际操作中，先画出仅接触曲线上所选点的切线，然后在切线上选取两个相距较远的点来计算其梯度。在切线上选取相距较远的点可以提高读数精度。

For example, if a tangent at t = 2 s passes through (1, 3) and (3, 7), the instantaneous velocity is v = (7 − 3) / (3 − 1) = 4 / 2 = 2 m/s. The smaller the time interval Δt around the chosen point, the closer the gradient is to the true instantaneous velocity.

例如，如果一条在 t = 2 s 处的切线经过点 (1, 3) 和 (3, 7)，则瞬时速度为 v = (7 − 3) / (3 − 1) = 4 / 2 = 2 m/s。所选点附近的时间间隔 Δt 越小，梯度就越接近真实的瞬时速度。

8. Comparing Motion Scenarios | 运动情形对比

The table below summarises the appearance of an s-t graph for different types of motion.

下表总结了不同类型运动对应的 s-t 图像特征。

Motion (运动类型)	Shape of s-t graph (图像形状)	Gradient / velocity (梯度/速度)
Stationary 静止	Horizontal line 水平线	Zero 零
Constant velocity, positive direction 正方向匀速	Straight line sloping up 向上倾斜直线	Positive constant 正的恒定值
Constant velocity, negative direction 反方向匀速	Straight line sloping down 向下倾斜直线	Negative constant 负的恒定值
Speeding up 加速	Curve becoming steeper 曲线变陡	Magnitude increasing 大小增大
Slowing down 减速	Curve becoming flatter 曲线变平缓	Magnitude decreasing 大小减小

Always remember that the gradient of an s-t graph tells you velocity, not acceleration. To find acceleration, you need a velocity-time graph, where gradient equals acceleration.

始终记住：s-t 图像的梯度告诉你的是速度，而不是加速度。要求加速度，需要使用速度-时间图像，其梯度等于加速度。

9. Worked Examples | 典型例题

Example 1: A cyclist starts at displacement 5 m from a fixed origin. She cycles to the 25 m mark in 4 s at constant velocity, waits 2 s, then cycles back to the origin in 4 s.

例题 1：一名骑车人从距固定原点 5 m 处出发，以恒定速度在 4 s 内骑到 25 m 处，停留 2 s，然后在 4 s 内返回原点。

(a) Stage 1 velocity: v = (s₂ − s₁) / (t₂ − t₁) = (25 − 5) / (4 − 0) = 20 / 4 = 5 m/s.

（a）第一阶段速度：v = (s₂ − s₁) / (t₂ − t₁) = (25 − 5) / (4 − 0) = 20 / 4 = 5 m/s。

(b) Stage 2 velocity: the graph is horizontal, so v = 0 m/s.

（b）第二阶段速度：图像水平，因此 v = 0 m/s。

(c) Stage 3 velocity: v = (0 − 25) / (10 − 6) = −25 / 4 = −6.25 m/s. The negative sign shows the cyclist is moving back towards the origin.

（c）第三阶段速度：v = (0 − 25) / (10 − 6) = −25 / 4 = −6.25 m/s。负号表示骑车人正在返回原点。

(d) Average velocity for the whole journey: total displacement = 0 − 5 = −5 m; total time = 10 s; v_avg = −5 / 10 = −0.5 m/s.

（d）全程平均速度：总位移 = 0 − 5 = −5 m；总时间 = 10 s；v_avg = −5 / 10 = −0.5 m/s。

Example 2: From a curved s-t graph, a tangent at t = 2 s passes through (1, 2) and (3, 6). The instantaneous velocity is v = (6 − 2) / (3 − 1) = 4 / 2 = 2 m/s. This means that, at exactly t = 2 s, the object is moving at 2 m/s in the positive direction.

例题 2：在一条弯曲的 s-t 图像上，t = 2 s 处的切线经过 (1, 2) 和 (3, 6)。瞬时速度为 v = (6 − 2) / (3 − 1) = 4 / 2 = 2 m/s。这意味着在 t = 2 s 的瞬间，物体以 2 m/s 的速度沿正方向运动。

10. Common Misconceptions and Exam Tips | 常见误区与应试技巧

Misconception 1: “A horizontal s-t graph means the object is at the origin.” This is false. A horizontal line only means the object is stationary; its displacement remains constant at whatever value the line shows.

误区 1：”s-t 图像为水平线表示物体在原点。”这是错误的。水平线只表示物体静止；无论水平线处于什么位移值，位移都保持不变。

Misconception 2: “A negative gradient means the object is slowing down.” This is false. A negative constant gradient means constant velocity in the negative direction. Slowing down is shown by a curve whose gradient magnitude decreases over time.

误区 2：”负梯度表示物体在减速。”这是错误的。负的恒定梯度表示沿负方向匀速运动。减速表现为曲线梯度的绝对值随时间减小。

Misconception 3: “A steeper graph always means greater acceleration.” This is false. The gradient of an s-t graph is velocity. A steep straight line means large velocity but zero acceleration because the gradient is not changing.

误区 3：”图像越陡表示加速度越大。”这是错误的。s-t 图像的梯度是速度。一条陡峭的直线表示速度大，但因为梯度不变，加速度为零。

Exam tips: Always include units such as m/s in your answers. Use the sign of the velocity to indicate direction. For curved graphs, draw a tangent and choose two widely separated points on it to minimise reading error. Read displacement values directly from the y-axis and never confuse them with distance travelled.

应试技巧：在答案中始终写明单位（如 m/s）。用速度的正负号表示方向。对于曲线，画出切线并在切线上选取两个相距较远的点以减小读数误差。直接从 y 轴读取位移值，切勿将其与运动路程混淆。

Finally, practise sketching graphs from descriptions of motion and describing motion from given graphs. This two-way translation will prepare you well for both multiple-choice and structured questions in the CIE exam.

最后，练习根据运动描述画出图像，以及根据给定图像描述运动。这种双向转换的能力将帮助你在 CIE 考试中的选择题和结构题中都取得好成绩。

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A-Level Physics: Interpreting Displacement-Time Graphs | A-Level 物理：位移-时间图像解读