📚 Displacement–time Graphs | 位移–时间图
Displacement–time graphs are fundamental tools in kinematics. They allow you to visualise an object's motion, determine its velocity from the gradient, and identify periods of rest or changing direction. Mastering these graphs is essential for success in CIE A–Level Physics, where they appear in both theory and practical examinations.
位移–时间图是运动学中的基本工具。它们能让你直观地观察物体的运动，通过斜率确定速度，并识别静止或改变方向的时段。掌握这些图线对于在 CIE A-Level 物理考试中取得好成绩至关重要，无论是理论还是实验考试都会涉及。
1. What is a Displacement–time Graph? | 什么是位移–时间图？
A displacement–time graph shows how the displacement of an object varies with time. The horizontal axis represents time t, and the vertical axis represents displacement s, which is a vector quantity measured from a chosen origin in metres (m). Positive displacement indicates the object is on one side of the origin, while negative displacement indicates it is on the opposite side. Note that this is not the same as a distance–time graph; distance is a scalar and cannot be negative.
位移–时间图展示了物体的位移如何随时间变化。横轴表示时间 t，纵轴表示位移 s；位移是矢量，从选定的原点量起，单位为米（m）。正位移表示物体位于原点的某一侧，负位移则表示在相反的一侧。请注意，它不同于路程–时间图，路程是标量，不能为负。
2. Displacement vs Distance: Why It Matters | 位移与路程：为何重要？
car travels from 0 m to 5 m in 2 s, then reverses to 2 m in the next 1 s, the displacement at t = 3 s is +2 m, but the total distance travelled is 8 m. A displacement–ime graph would show a line rising to 5 m and then sloping down to 2 m, whereas a distance–time graph would only show a rising curve. In CIE A– sics, you must always check whether the vertical axis represents displacement or distance.
当物体先向前运动再返回时，位移会改变符号，而路程只会增加。例如，一辆玩具车在 2 秒内从 0 m 运动到 5 m，然后在接下来的 1 秒内倒回至 2 m，第 3 秒时的位移是 +2 m，但走过的总路程是 8 m。位移–时间图会显示一条线先上升到 5 m，然后向下倾斜到 2 m，而路程–时间图则会持续上升。在 CIE A-Level 物理中，务必确认纵轴是位移还是路程。
3. Plotting a Displacement–time Graph | 绘制位移–时间图
To plot a displacement–time graph, place time on the x‑axis and displacement on the y‑axis. Choose a convenient scale and label both axes with quantities and units, e.g. t / s and s / m. Mark the data points and join them with straight lines or a smooth curve depending on the type of motion. The origin (0,0) may not always be a data point, but it is good practice to include it when time starts from zero. The graph can start at a non‑zero displacement if the object does not begin at the origin.
绘制位移–时间图时，将时间放在 x 轴，位移放在 y 轴。选择合适的刻度，并用物理量和单位标注坐标轴，如 t / s 和 s / m。标出数据点，然后根据运动类型用直线或光滑曲线连接。原点 (0,0) 不一定总是数据点，但如果时间从零开始，最好包含原点。若物体不是从原点出发，图像可从非零位移处开始。
4. The Slope Equals Velocity | 斜率等于速度
The most important feature of a displacement–time graph is that its gradient (slope) gives the velocity of the object. For any time interval, average velocity vavg lacement and Δt is the time taken. If the graph is a straight line, the gradient is constant, so the velocity is uniform. A steeper line means a larger velocity. Velocity is a vector; its direction is shown by the sign of the slope.
位移–时间图最重要的特征是斜率（梯度）给出物体的速度。对于任意时间间隔，平均速度 vavg = Δs / Δt，其中 Δs 是位移变化量，Δt 是所用时间。若图像为一条直线，斜率恒定，速度即为匀速。越陡的线表示速度越大。速度是矢量，其方向由斜率的正负号表示。
5. Positive and Negative Slope | 正斜率和负斜率
If the line slopes upwards from left to right, the slope is positive, indicating that the object is moving in the positive direction (away from the origin). If the line slopes downwards, the slope is negative, and the object is moving in the negative direction (towards the origin or past it). A line that becomes steeper in a positive sense means an increasing velocity in the positive direction; a line that flattens means a decreasing speed.
如果线条从左到右向上倾斜，斜率为正，表示物体沿正方向运动（远离原点）。若线条向下倾斜，斜率为负，物体沿负方向运动（朝向原点或越过原点）。正斜率的线变得更陡表示正方向速度增大；线条趋于平缓则表示速率减小。
6. Constant Velocity Motion | 匀速直线运动
When an object moves with constant velocity, its displacement– t produces a straight line with a slope of +10 m s⁻¹. The displacement increases by 10 m each second. The equation of the line is s = v t + s₀, where s₀ is the initial displacement.
当物体做匀速直线运动时，其位移–时间图为一条直线，斜率保持不变。例如，一辆汽车以 10 m s⁻¹ 的恒定速度向正方向远离出发点，其图线为斜率 +10 m s⁻¹ 的直线，位移每秒钟增加 10 m。图线方程可写为 s = v t + s₀，其中 s₀ 是初始位移。
7. Stationary Objects: Zero Slope | 静止物体：零斜率
ty is zero. The line lies at a fixed displacement value. For example, if a cyclist stops at a position 20 m from the start for 5 seconds, the graph shows a horizontal line at s = 20 m between the appropriate times.
若物体静止，位移不随时间改变，图线为一条水平直线。斜率为零，意味着速度为零。该直线位于某一固定位移值。例如，一名骑车人在距起点 20 m 处停了 5 秒钟，其图线在相应时间段内显示为 s = 20 m 的水平线。
8. Curved Graphs and Acceleration | 曲线图与加速度
A curved displacement–time graph indicates that the velocity is changing, i.e. the object is accelerating or decelerating. If the curve becomes steeper over time, the speed is increasing; if the curve flattens, the speed is decreasing. To determine whether the object is accelerating in the same direction as its motion, compare the sign of the slope and the sign of its change. For instance, a curve with a positive slope that is getting steeper means the object is moving in the positive direction and speeding up (positive acceleration). A curve with a positive slope that is levelling off means it is still moving forward but slowing down (negative acceleration).
曲线形的位移–时间图表明速度在变化，即物体在加速或减速。若曲线随时间推移变得更陡，则速率在增大；若曲线趋于平缓，则速率在减小。要判断加速度方向是否与运动方向相同，需比较斜率及其变化量的正负。例如，一条拥有正斜率且越来越陡的曲线，表示物体朝正方向运动且加速（加速度为正）。一条正斜率但趋于水平的曲线，表示物体仍向前运动但减速（加速度为负）。
9. Finding Instantaneous Velocity: Tangent | 求瞬时速度：切线
For a curved displacement–time graph, the average velocity between two points is given by the chord slope, but the instantaneous velocity at a specific time is found by drawing a tangent to the curve at that point. A tangent is a straight line that just touches the curve and has the same gradient as the curve at that instant. Choose two widely separated points on the tangent to calculate its slope accurately: vinst Δt (using the tangent). This method is widely tested in CIE practical and written papers.
对于曲线位移–时间图，两点之间的平均速度由弦的斜率给出，但某一特定时刻的瞬时速度需通过在该点作切线求得。切线是与曲线相切且在该瞬间与曲线梯度相同的直线。在切线上选取两个相隔较远的点，以准确计算斜率：vinst = Δs / Δt（使用切线上的变化量）。这种方法在 CIE 的实验和笔试中经常考查。
10. Average Velocity versus Instantaneous Velocity | 平均速度与瞬时速度
On any displacement–time graph, the average velocity over an interval is the slope of the straight line joining the start and end points of that interval. For a curved graph, this chord slope differs from the instantaneous velocity at most times. For example, if a runner starts and finishes at the same point (displacement zero), the average velocity for the whole trip is zero, but the instantaneous velocity was non‑zero during the run. The tangent slope reveals the actual velocity at each moment. Published by TutorHao | A-Level Physics Revision Series | aleveler.com
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