📚 Mastering Motion Graphs: Displacement-Time and Velocity-Time Graphs | 掌握运动图像：位移-时间图与速度-时间图
Motion graphs are among the most important analytical tools in Edexcel A-Level Physics Topic 2.2.1. You must be able to draw, interpret and convert displacement-time and velocity-time graphs, and use gradients and areas to calculate physical quantities. This skill appears in almost every mechanics exam and is the foundation for understanding acceleration, projectiles, forces and energy.
运动图像是 Edexcel A-Level 物理 Topic 2.2.1 中最重要的分析工具之一。你必须能够绘制、解释和转换位移-时间图与速度-时间图，并利用斜率和面积计算物理量。这个技能几乎出现在每次力学考试中，是理解加速度、抛体运动、力和能量的基础。
1. Why Motion Graphs Matter | 为什么运动图像重要
Graphs give a compact, visual way to describe motion without writing long tables of data. In A-Level Physics, a displacement-time graph tells you where an object is, while a velocity-time graph tells you how quickly and in what direction it is moving. Examiners frequently ask you to calculate gradients, identify areas, and sketch one graph from another.
图像提供了一种简洁、直观的方式来描述运动，而无需写出冗长的数据表。在 A-Level 物理中，位移-时间图告诉你物体在哪里，而速度-时间图告诉你物体运动得多快以及朝哪个方向运动。考官经常要求你计算斜率、识别面积，并根据一种图像画出另一种图像。
Understanding these graphs is not just an isolated skill. The same ideas of gradient and area under a curve reappear in contexts such as current-charge graphs, force-extension graphs and terminal velocity. Mastering them early in mechanics makes later topics much easier.
理解这些图像不仅仅是一项孤立的技能。斜率和曲线下面积的思想会重新出现在电流-电荷图、力-伸长图以及终极速度等情境中。在力学早期就掌握这些内容，会让后面的主题变得容易得多。
2. Scalar and Vector Quantities | 标量与矢量
Before drawing any graph, you must distinguish between distance and displacement, and between speed and velocity. Distance is a scalar quantity: it only has magnitude and is always positive. Displacement is a vector: it has both magnitude and direction, so it can be positive, negative or zero depending on the chosen reference point.
在绘制任何图像之前，你必须区分距离和位移，以及速率和速度。距离是标量：它只有大小，并且总是正的。位移是矢量：它既有大小又有方向，因此根据所选参考点，它可以是正的、负的或零。
On a displacement-time graph, the vertical axis usually represents displacement from a fixed origin in metres. A positive value means the object is on one side of the origin, while a negative value means it is on the opposite side. In the same way, velocity can be positive or negative, so a velocity-time graph can dip below the time axis.
在位移-时间图中，纵轴通常表示物体相对于固定原点的位移，单位为米。正值表示物体位于原点的一侧，而负值表示物体位于相反的一侧。同样，速度也可以是正的或负的，因此速度-时间图可以下降到时间轴以下。
3. Reading Displacement-Time Graphs | 阅读位移-时间图
A displacement-time graph, often written as an s-t graph, plots displacement s on the vertical axis and time t on the horizontal axis. Each point on the line shows the object’s displacement at a particular time. The shape of the line tells you whether the object is stationary, moving at constant velocity, or accelerating.
位移-时间图通常写作 s-t 图，其纵轴为位移 s，横轴为时间 t。图线上的每个点表示物体在某一时刻的位移。图线的形状告诉你物体是静止的、匀速运动的还是加速运动的。
The average velocity over an interval is found using the gradient of the straight chord connecting the two points.
某一时间间隔内的平均速度可以通过连接两个点的直线弦的斜率求出。
v = Δs / Δt = (s₂ – s₁) / (t₂ – t₁)
For example, if an object moves from displacement 5 m at t = 2 s to displacement 20 m at t = 7 s, the average velocity is (20 – 5) / (7 – 2) = 15 / 5 = 3 m s⁻¹.
例如，如果物体在 t = 2 s 时位移为 5 m，在 t = 7 s 时位移为 20 m，则平均速度为 (20 – 5) / (7 – 2) = 15 / 5 = 3 m s⁻¹。
| Graph feature | Meaning |
| Horizontal line | Stationary object at fixed displacement |
| Straight sloping line | Constant velocity; gradient gives velocity |
| Curved line | Changing velocity, hence acceleration |
| Positive gradient | Positive velocity, increasing displacement |
| Negative gradient | Negative velocity, decreasing displacement |
4. Velocity from Gradients | 从斜率求速度
The gradient of a displacement-time graph represents velocity. For a straight line, the gradient is constant, so the velocity is uniform. For a curved line, the gradient changes from point to point, so you must draw a tangent to the curve to find the instantaneous velocity at that point.
位移-时间图的斜率表示速度。对于直线，斜率是恒定的，因此速度是匀速的。对于曲线，斜率逐点变化，因此你必须画出曲线在该点的切线，才能求出该点的瞬时速度。
To calculate a tangent gradient, pick two well-separated points on the tangent, read their coordinates, and use the same rise-over-run formula. Do not use two points from the curve itself unless the line is straight, because that only gives average velocity.
要计算切线斜率，请在切线上选取两个相距较远的点，读取它们的坐标，并使用相同的“垂直变化除以水平变化”公式。除非图线是直线，否则不要使用曲线本身的点，因为那样只能得到平均速度。
instantaneous velocity = gradient of tangent
In an exam, show your tangent construction clearly. The gradient should be written with correct units, normally m s⁻¹. If the gradient is negative, the object is moving in the negative direction.
在考试中，请清楚地展示切线的作图过程。斜率应写出正确的单位，通常是 m s⁻¹。如果斜率为负，则物体正朝负方向运动。
5. Reading Velocity-Time Graphs | 阅读速度-时间图
A velocity-time graph, or v-t graph, plots velocity v on the vertical axis and time t on the horizontal axis. The value of the line at any instant tells you the object’s velocity. A positive value means one direction, a negative value means the opposite direction, and zero means the object is momentarily at rest.
速度-时间图，即 v-t 图，其纵轴为速度 v，横轴为时间 t。图线在任意时刻的值告诉你物体的速度。正值表示一个方向，负值表示相反方向，零表示物体瞬间静止。
| Graph feature | Meaning |
| Horizontal line above axis | Constant positive velocity, no acceleration |
| Horizontal line below axis | Constant negative velocity |
| Straight sloping line | Constant acceleration; gradient gives acceleration |
| Curved line | Changing acceleration |
| Line crossing time axis | Object changes direction |
For uniform motion, a velocity-time graph is a horizontal line because velocity does not change. For uniform acceleration, the graph is a straight sloping line. The steeper the slope, the greater the magnitude of acceleration.
对于匀速运动，速度-时间图是一条水平线，因为速度不变。对于匀加速运动，图线是一条倾斜的直线。斜率越大，加速度的大小就越大。
6. Acceleration from Gradients | 从斜率求加速度
The gradient of a velocity-time graph gives acceleration. A positive gradient means positive acceleration in the chosen direction; a negative gradient means negative acceleration, often called deceleration or retardation if the speed is decreasing.
速度-时间图的斜率表示加速度。正斜率表示沿所选方向的正加速度；负斜率表示负加速度，如果速率在减小，通常称为减速或滞动。
a = Δv / Δt = (v₂ – v₁) / (t₂ – t₁)
For instance, if a cyclist’s velocity changes from 4 m s⁻¹ to 12 m s⁻¹ in 8 seconds, the acceleration is (12 – 4) / 8 = 8 / 8 = 1 m s⁻². This means the velocity increases by 1 metre per second every second.
例如，如果骑自行车者的速度在 8 秒内从 4 m s⁻¹ 变为 12 m s⁻¹，则加速度为 (12 – 4) / 8 = 8 / 8 = 1 m s⁻²。这意味着速度每秒增加 1 米每秒。
Always include the unit m s⁻² when giving acceleration. If the velocity values are in opposite directions, make one positive and the other negative before subtracting.
给出加速度时，请始终包含单位 m s⁻²。如果速度方向相反，则先将其中一个取正、另一个取负，然后再相减。
7. Area Under Velocity-Time Graphs | 速度-时间图下面积
The area between a velocity-time line and the time axis represents displacement. This is one of the most useful ideas in mechanics. Areas above the time axis give positive displacement; areas below the axis give negative displacement. The total displacement is the algebraic sum of all areas.
速度-时间图线与时间轴之间的面积表示位移。这是力学中最有用的思想之一。时间轴上方的面积给出正位移；时间轴下方的面积给出负位移。总位移是所有面积的代数和。
For simple shapes, use standard area formulas. A rectangle has area base × height. A triangle has area ½ × base × height. A trapezium, common for uniform acceleration from an initial velocity u to a final velocity v, has area ½ × (u + v)
Published by TutorHao | A-Level Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply