Displacement–Time Graphs | 位移–时间图

📚 Displacement–Time Graphs | 位移–时间图

Displacement–time graphs are one of the first tools you meet in A-Level Physics. They show how an object’s displacement from a fixed origin changes over time, and their gradients reveal velocity. Mastering these graphs is essential for Edexcel mechanics and for describing motion in one dimension.

位移–时间图是你在 A-Level 物理中最早接触的工具之一。它们展示物体相对于固定原点的位移如何随时间变化，而图线的斜率则揭示速度。掌握这些图对 Edexcel 力学以及描述一维运动至关重要。

1. What is Displacement? | 什么是位移？

Displacement is a vector quantity. It measures the straight-line distance from a chosen origin in a specified direction. It is not the same as distance, which is scalar and only counts how much ground is covered.

位移是一个矢量。它测量从选定原点出发、沿指定方向的直线距离。它与路程不同，路程是标量，只计算物体经过的总长度。

For example, if a runner goes 100 m east and then 40 m west, the total distance is 140 m, but the displacement is 60 m east.

例如，一名跑步者先向东跑 100 m，再向西跑 40 m，总路程为 140 m，但位移为向东 60 m。

2. Reading a Displacement–Time Graph | 阅读位移–时间图

On a displacement–time graph, time t is plotted on the horizontal axis and displacement s from the origin is plotted on the vertical axis. The origin is usually chosen at a convenient starting point.

在位移–时间图中，时间 t 画在横轴，位移 s 画在纵轴。原点通常选在方便的位置。

A point on the curve gives the object’s displacement at a particular time. A horizontal line means the displacement is not changing, so the object is stationary.

图线上的某一点给出物体在某一时刻的位移。水平线表示位移不变，因此物体静止。

3. Gradient = Velocity | 斜率 = 速度

The gradient of a displacement–time graph equals velocity. Since velocity is a vector, the sign of the gradient tells you the direction of motion.

位移–时间图的斜率等于速度。由于速度是矢量，斜率的正负号告诉你运动方向。

Mathematically, velocity v = Δs / Δt, where Δs is the change in displacement and Δt is the change in time.

数学上，速度 v = Δs / Δt，其中 Δs 是位移的变化量，Δt 是时间的变化量。

v = Δs / Δt

A steeper gradient means a larger speed. If the gradient is positive, velocity is in the positive direction; if negative, velocity is in the negative direction.

斜率越陡，速率越大。如果斜率为正，速度沿正方向；如果斜率为负，速度沿负方向。

4. Average Velocity: The Secant Line | 平均速度：割线

To find the average velocity between two instants t₁ and t₂, draw a straight line connecting the two points on the curve. This line is called a secant. Its gradient is the average velocity over that interval.

要求两个时刻 t₁ 和 t₂ 之间的平均速度，请在图线上连接这两点作一条直线。这条线称为割线。它的斜率就是该时间段内的平均速度。

Average velocity = (s₂ − s₁) / (t₂ − t₁). This value does not describe what happened at every moment, only the overall change.

平均速度 = (s₂ − s₁) / (t₂ − t₁)。这个数值并不描述每一瞬间的情况，只描述整体变化。

v_avg = (s₂ − s₁) / (t₂ − t₁)

5. Instantaneous Velocity: The Tangent | 瞬时速度：切线

For the velocity at a single instant, draw a tangent to the curve at that point. The gradient of the tangent is the instantaneous velocity.

对于某一瞬间的速度，请在该点作曲线的切线。切线的斜率就是瞬时速度。

On a straight-line graph, the tangent is just the graph itself, so velocity is constant. On a curved graph, the tangent changes from point to point.

在直线图上，切线就是图线本身，因此速度恒定。在曲线图上，切线逐点变化。

6. Constant Velocity Motion | 匀速直线运动

If an object moves with constant velocity, the displacement–time graph is a straight line with a non-zero gradient. Equal time intervals produce equal changes in displacement.

如果物体以恒定速度运动，位移–时间图是一条斜率不为零的直线。相等的时间间隔产生相等的位移变化。

The equation of such a line is s = ut + s₀, where u is the constant velocity and s₀ is the initial displacement.

这条直线的方程为 s = ut + s₀，其中 u 是恒定速度，s₀ 是初始位移。

s = ut + s₀

A straight line sloping upward means constant positive velocity; a straight line sloping downward means constant negative velocity.

向上倾斜的直线表示恒定的正速度；向下倾斜的直线表示恒定的负速度。

7. Acceleration and Curved Graphs | 加速度与曲线图

If velocity is changing, the displacement–time graph is curved. The gradient at any point is the instantaneous velocity, and the curvature shows acceleration.

如果速度在变化，位移–时间图就是曲线。任意一点的斜率是瞬时速度，而曲线的弯曲程度显示加速度。

For constant acceleration, the graph is a parabola because displacement depends on t². The equation is s = ut + ½at² + s₀.

对于恒定加速度，图线是抛物线，因为位移依赖于 t²。其方程为 s = ut + ½at² + s₀。

s = ut + ½at² + s₀

A curve that becomes steeper with time means speeding up in the positive direction. A curve that flattens means slowing down.

随时间变陡的曲线表示沿正方向加速。逐渐变平的曲线表示减速。

8. Positive and Negative Displacement | 正位移与负位移

Displacement can be positive or negative depending on the chosen positive direction. Values above the time axis are positive; values below are negative.

位移可为正也可为负，取决于所选的正方向。时间轴上方的值为正，下方的值为负。

Negative displacement does not necessarily mean moving backwards; it means the object is on the negative side of the origin. The sign of the gradient determines the direction of motion.

负位移并不一定表示向后运动；它表示物体位于原点的负侧。斜率的正负才决定运动方向。

When the graph crosses the time axis, the object passes through the origin.

当图线穿过时间轴时，物体经过原点。

9. Turning Points and Changes of Direction | 转折点与改变方向

A turning point occurs where the gradient changes sign, such as at a maximum or minimum on the displacement–time graph. At that instant, velocity is zero.

转折点出现在斜率改变符号的地方，例如位移–时间图上的极大值或极小值。在这一瞬间，速度为零。

If the graph goes from positive gradient to negative gradient, the object reverses direction. The point where the tangent is horizontal is the moment of reversal.

如果图线从正斜率变为负斜率，物体就反向运动。切线水平的那一点就是反向的时刻。

On a smooth curve, the turning point is where the tangent is horizontal. The displacement is momentarily at a maximum or minimum.

在光滑曲线上，转折点处切线水平。位移暂时达到极大值或极小值。

10. Comparing Displacement–Time and Distance–Time | 位移–时间图与距离–时间图比较

A distance–time graph can only increase or stay flat because distance is scalar and never decreases. A displacement–time graph can slope down when the object moves towards the origin.

距离–时间图只能上升或保持水平，因为路程是标量，永远不会减少。位移–时间图可以在物体朝向原点运动时向下倾斜。

Because of this, distance–time graphs hide direction, while displacement–time graphs show it through the sign of the gradient.

因此，距离–时间图隐藏方向信息，而位移–时间图通过斜率的正负显示方向。

When a journey involves returning to the start, the distance–time graph ends at a high value, but the displacement–time graph ends at zero.

当一段旅程包含返回起点时，距离–时间图最终处于较高值，而位移–时间图最终回到零。

11. Common Misconceptions | 常见误区

Mistake 1: thinking that a negative gradient means negative displacement. The gradient gives velocity, not displacement. A negative gradient means moving in the negative direction.

误区一：认为负斜率表示负位移。斜率给出的是速度，而不是位移。负斜率表示沿负方向运动。

Mistake 2: reading the y-value as distance travelled. The y-axis is displacement, so it can decrease and does not show total path length.

误区二：把纵坐标值看成已走过的路程。纵轴是位移，它会减少，并且不显示总路径长度。

Mistake 3: assuming a straight horizontal line means the object is at the origin. It means the object is stationary at whatever displacement the line is at.

误区三：认为水平直线表示物体在原点。它表示物体静止于该直线所在的位移处。

12. Exam Tips for Edexcel A-Level | Edexcel A-Level 考试技巧

In Edexcel mechanics questions, you may be asked to sketch, interpret, or calculate gradients of displacement–time graphs. Always label axes with quantities and units, and show a large tangent triangle when finding instantaneous velocity.

在 Edexcel 力学题中，你可能会被要求画草图、解读或计算位移–时间图的斜率。务必在坐标轴上标注物理量和单位，并在求瞬时速度时画出足够大的切线三角形。

When calculating a gradient, use two well-separated points on the tangent to reduce uncertainty. Quote the velocity with a sign and unit, such as +6.0 m s⁻¹.

计算斜率时，在切线上选择两个相距较远的点以减小误差。速度要带正负号和单位，例如 +6.0 m s⁻¹。

If a graph has multiple straight-line sections, describe each section separately: stationary, constant positive velocity, constant negative velocity, and so on.

如果图线由多段直线组成，请分别描述每一段：静止、恒定正速度、恒定负速度等。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Displacement–Time Graphs | 位移–时间图