📚 IB AQA Physics: Kinematics Key Concepts | IB AQA 物理：运动学考点精讲
Welcome to this in-depth revision guide on kinematics, tailored for students studying IB Physics or following the AQA examination board. Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion. In this article, we will systematically break down every key concept—from scalars and vectors to the equations of motion, graphs, and projectile motion—with clear explanations, examples, and exam tips. Whether you are preparing for Paper 1 multiple-choice questions, Paper 2 structured problems, or your IB internal assessment, mastering kinematics will give you a solid foundation for the rest of the physics course.
欢迎阅读这份详尽的运动学考点精讲，专为学习IB物理或参加AQA考试的学生设计。运动学是力学的一个分支，它描述物体的运动情况，但不追究引起运动的力。本文将系统地分解每一个核心概念——从标量和矢量，到运动方程、图像分析和抛体运动——包含清晰的解释、例题和应试技巧。无论你是在为Paper 1选择题、Paper 2结构化问题还是IB内部评估做准备，扎实掌握运动学将为后续物理课程打下坚实基础。
1. Scalars and Vectors | 标量与矢量
In kinematics, all measurable quantities fall into two categories: scalars are physical quantities that have magnitude only, such as distance, speed, mass, and time. Vectors, on the other hand, have both magnitude and direction, and are represented by arrows or boldface symbols. Displacement, velocity, acceleration, and force are vectors. When adding vectors, you must consider their direction; two vectors in the same direction are added, while those in opposite directions subtract. Perpendicular vectors require the parallelogram or triangle method, often leading to the use of Pythagoras' theorem and trigonometry to find the resultant magnitude and direction.
在运动学中，所有可测量的物理量分为两类：标量是只有大小的物理量，例如距离、速率、质量和时间。矢量则同时具有大小和方向，通常用箭头或粗体符号表示。位移、速度、加速度和力都是矢量。矢量相加时必须考虑方向；同向的矢量直接相加，反向的矢量相减。相互垂直的矢量需要使用平行四边形法则或三角形法则进行合成，通常要使用勾股定理和三角函数求合矢量的大小和方向。
For example, if a student walks 3.0 m east and then 4.0 m north, the total distance travelled is 7.0 m (a scalar), but the displacement is 5.0 m at an angle of 53° north of east. The displacement vector is the straight-line distance from start to finish. In exam questions, always be careful to distinguish between 'distance' and 'displacement', and between 'speed' and 'velocity'. A common trick: if an object moves in a circle and returns to its starting point, its displacement is zero, but distance is the circumference of the circle.
例如，一名学生向东走了3.0 m再向北走了4.0 m，所走过的路程是7.0 m（标量），但位移大小为5.0 m，方向为东偏北53°。位移矢量是从起点到终点的直线距离。在考试中，一定要留意区分“距离”和“位移”，以及“速率”和“速度”。一个常见陷阱：如果物体绕圆周运动回到起点，它的位移为零，但路程等于圆周长。
2. Displacement, Velocity and Acceleration | 位移、速度和加速度
Displacement s is defined as the change in position of an object, and its SI unit is the metre (m). It is a vector pointing from the initial position to the final position. Average velocity is the rate of change of displacement: vavg he limit of average velocity as the time interval approaches zero, which corresponds to the gradient of a displacement–time graph. Speed is the magnitude of velocity, so it is always positive.
位移 s 定义为物体位置的变化，其国际单位是米(m)。它是一个矢量，方向由初位置指向末位置。平均速度是位移的变化率：vavg = Δs / Δt。瞬时速度是当时间间隔趋近于零时平均速度的极限，在位移–时间图像上等于切线的斜率。速率是速度的大小，因此总是正值。
t is m s⁻². Because velocity is a vector, acceleration can be caused by a change in speed, a change in direction, or both. In uniform circular motion, the speed is constant, yet there is a centripetal acceleration directed towards the centre because the direction of velocity is continuously changing. In linear kinematics with constant acceleration, we often use the SUVAT equations.
加速度 a 是速度的变化率，即 a = Δv / Δt。其单位是 m s⁻²。由于速度是矢量，加速度可以由速率变化、方向变化或两者共同引起。在匀速圆周运动中，速率恒定，但由于速度方向不断变化，存在指向圆心的向心加速度。在匀变速直线运动中，我们通常使用SUVAT方程。
3. Equations of Motion (SUVAT) | 运动方程（SUVAT）
When an object moves in a straight line with constant acceleration, the five fundamental equations link five quantities: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). These are often called the SUVAT equations. They can only be used when the acceleration is uniform and motion is along a straight line. Each equation misses one variable, which allows you to select the one that fits the given data.
当物体沿直线做匀变速运动时，五个基本方程联系着五个物理量：s（位移）、u（初速度）、v（末速度）、a（加速度）和 t（时间），通常被称为SUVAT方程。它们只有在加速度恒定且运动沿直线时才能使用。每个方程都缺少一个变量，因此你能根据已知量选择合适的方程。
v = u + at | s = ½(u+v)t | v² = u² + 2as
s = ut + ½ at² | s = vt − ½ at²
| Equation | Missing variable | equation |
|---|---|---|
| v = u + at | s | v = u + at |
| s = ½(u+v)t | a | s = ½(u+v)t |
| v² = u² + 2as | t | v² = u² + 2as |
| s = ut + ½ at² | v | s = ut + ½ at² |
| s = vt − ½ at² | u | s = vt − ½ at² |
or left has negative velocity. Gravity acting downwards is usually assigned a = −9.81 m s⁻² when upward is positive. Mixing up signs is one of the most frequent mistakes in kinematics. Work stepwise: list the five symbols, fill in the three knowns and the unknown, then pick the equation that connects them.
解题前一定要建立明确的正方向。通常把向上或向右选为正；那么向下或向左运动的物体速度为负。重力加速度方向向下，当向上为正时，通常取 a = −9.81 m s⁻²。符号混乱是运动学中最常见的错误之一。解题要分步走：列出五个符号，填入三个已知量和未知量，然后选择能把它们联系起来的方程。
4. Free Fall and Vertical Motion under Gravity | 自由落体与竖直抛体运动
Free fall is a special case of constant acceleration where the only force acting on the object is gravity, and we neglect air resistance. The acceleration due to gravity, g, is approximately 9.81 m s⁻² near the Earth's surface and is directed downwards. In most exam problems, you treat g as 9.8 or 9.81 m s⁻² and always remember to use a negative sign for a when upward is positive.
自由落体是匀变速直线运动的一个特例，运动中物体只受重力作用，并且忽略空气阻力。重力加速度 g 在地球表面附近约为 9.81 m s⁻²，方向向下。在大多数考题中，g 取 9.8 或 9.81 m s⁻²，并切记当向上为正时 a 必须带负号。
m height using v = u + at → 0 = u − gt, giving t = u/g. Maximum height can be found from v² = u² + 2as, yielding s = u²/(2g). Note that the time taken to go up equals the time to come down if the launch and landing points are at the same height, because symmetry holds in the absence of air resistance.
对于以初速度 u 竖直上抛的物体，当末速度 v = 0 时达到最高点。可由 v = u + at → 0 = u − gt 求出到达最高点的时间 t = u/g。最高点的高度可由 v² = u² + 2as 得出 s = u²/(2g)。注意：若抛点和落点在同一高度，上升时间和下落时间相等，这是因为在没有空气阻力时运动具有对称性。
5. Projectile Motion | 斜抛与平抛运动
Projectile motion is two-dimensional motion with constant gravitational acceleration downward and no acceleration horizontally (ignoring air resistance). The key is to resolve the initial velocity into horizontal and vertical components: ux = u cos θ, uy = u sin θ. The horizontal motion is uniform, so horizontal displacement is given by x = ux ion is governed by the SUVAT equations with a = −g or +g depending on the sign convention.
抛体运动是一种二维运动，竖直方向有恒定的重力加速度，而水平方向没有加速度（忽略空气阻力）。解题的关键是将初速度分解为水平和竖直分量：ux = u cos θ，uy = u sin θ。水平方向做匀速直线运动，位移 x = ux t。竖直方向使用SUVAT方程，a = −g 或 +g 视正方向而定。
tile launched and landing on the same horizontal level, the total time of flight is T = 2uy/g. The maximum height is H = uy urs when the launch angle is 45° (in the absence of air resistance). Exam questions often combine energy considerations with kinematics, or involve projectiles fired from a height.
抛体的轨迹为抛物线。飞行时间只取决于竖直方向的运动。对于从地面抛出又落回同一水平面的抛体，总飞行时间 T = 2uy/g，最大高度 H = uy²/(2g)，水平射程 R = (u² sin 2θ)/g。当抛出角为45°时射程最远（忽略空气阻力）。考试中经常会将能量和运动学结合，或考查从一定高度抛出的物体。
6. Displacement–Time Graphs | 位移–时间图像
A displacement–time graph plots displacement on the vertical axis against time on the horizontal axis. The gradient at any point gives the instantaneous velocity. A straight line with a positive slope indicates constant positive velocity; a horizontal line means the object is at rest (zero velocity); a curved line implies changing velocity, i.e., acceleration. You must be able to sketch, interpret, and extract information from these graphs in both multiple-choice and extended-response questions.
位移–时间图的纵轴是位移，横轴是时间。图线上任一点的斜率代表瞬时速度。斜线向上且为直线表示物体以恒定的正速度运动；水平线表示物体静止（速度为零）；曲线表示速度在变化，即物体在加速或减速。你必须能够在选择题和简答题中绘制、解读这类图像，并从中提取信息。
If the graph curves upwards, the slope is increasing, meaning acceleration is positive. Downward curving suggests negative acceleration (deceleration if moving in positive direction). In IB and AQA exams, you may be given a velocity–time graph and asked to sketch the corresponding displacement–time graph, or vice versa. Remember that displacement can become negative if the object moves past the origin in the opposite direction. The total distance travelled is not shown directly unless you compute the absolute area under a velocity–time graph.
如果图线向上弯曲，斜率增大，表示正加速度。向下弯曲表示负加速度（若沿正方向运动则为减速）。在IB和AQA考试中，可能会给出速度–时间图，让你画出对应的位移–时间图，或者反之。记住：当物体越过原点向负方向运动时，位移可以变为负值。路程并不直接显示在位移–时间图上，而需要借助速度–时间图下的绝对值面积计算。
7. Velocity–Time Graphs | 速度–时间图像
The velocity–time graph is the most powerful graphical tool in kinematics. The gradient gives the acceleration; the area between the graph and the time axis represents displacement (with signs). If the graph lies above the time axis, velocity is positive; below is negative. A constant positive acceleration produces a straight sloping line upward. A zero gradient means constant velocity. A changing gradient signifies a non-uniform acceleration, which often appears in exam questions about terminal velocity or resistive forces.
速度–时间图是运动学中最强大的图像工具。图线的斜率代表加速度；图线与时间轴围成的面积代表位移（带符号）。图线在时间轴上方表示速度为正，下方为负。恒定的正加速度产生一条向上倾斜的直线。斜率为零表示匀速运动。斜率变化意味着加速度不均匀，经常出现在涉及终极速度或阻力的考题中。
(if given a function) may be required. In multi-step problems, you can combine a velocity–time graph with the SUVAT equations. For example, the area under a velocity– over time t is exactly s = ½(u+v)t, which is the area of a trapezium. Practise sketching v–t graphs for bouncing balls and objects thrown upwards.
计算面积时可把区域分割成矩形、三角形或梯形。对于曲线，可能需要采用格点计数或积分（若给出函数）。在多步问题中，可将速度–时间图与SUVAT方程结合使用。例如，初速度 u 到末速度 v 的匀变速直线运动所对应的速度–时间图下面积恰好是 s = ½(u+v)t，即梯形的面积。建议多练习反弹球和竖直上抛物体的 v–t 图像绘制。
8. Acceleration–Time Graphs | 加速度–时间图像
An acceleration– is a horizontal line, and the area is a rectangle: Δv = a × t. If the acceleration changes linearly, the area is a triangle or trapezium. When acceleration is zero, the graph lies on the time axis. These graphs are less common in basic kinematics but appear in topics like simple harmonic motion and thrust curves in rocket motion.
加速度–时间图以时间为横轴、加速度为纵轴。图线下方的面积等于速度的变化量：Δv = ∫ a dt。匀变速运动中，图线是一条水平线，面积即为矩形：Δv = a × t。若加速度线性变化，面积可以是三角形或梯形。零加速度时图线与时间轴重合。加速度–时间图在基础运动学中较少见，但会出现在简谐运动或火箭推力曲线等内容中。
9. Relative Velocity (AQA and IB Context) | 相对速度（AQA与IB考点）
Relative velocity is the velocity of one object as observed from another object. If two objects A and B are moving with velocities vA and vB relative to the ground, the velocity of A relative to B is vAB = vA − vB. This vector subtraction is essential in problems involving river currents, aircraft flying in wind, or two cars overtaking. AQA and IB syllabi often include one-dimensional relative motion for calculations and graphical vector addition for two dimensions.
相对速度是指从另一个物体上观察到某物体的速度。若A和B相对地面的速度分别为 vA 和 vB，则A相对于B的速度为 vAB = vA − vB。这种矢量减法在涉及河流流速、飞机在风中飞行或两车超车等问题中至关重要。AQA和IB大纲通常会包含一维相对运动的计算以及二维矢量合成的图形方法。
For a boat crossing a river, the resultant velocity relative to the bank is the vector sum of the boat's velocity relative to the water and the water's velocity relative to the bank. The time to cross depends only on the component of the boat's velocity perpendicular to the flow, while the downstream drift depends on the parallel component and the river speed. Always draw a clear vector diagram and use trigonometry to find the magnitude and direction.
对于渡河问题，船相对于河岸的合速度是船相对于水的速度与水相对于河岸的速度的矢量和。渡河时间仅取决于船速垂直于水流的分量，而下游的漂移量则取决于平行分量和水流速度。务必画出清晰的矢量图，并用三角函数求合速度的大小和方向。
10. Common Exam Pitfalls and Tips | 常见失分点与应试技巧
s (displacement, velocity, acceleration) must follow that convention. For upward-launched projectiles, using a = +g after setting upward as positive is a classic error. Always write down your sign convention before beginning a calculation. Another pitfall is using the SUVAT equations when acceleration is not constant—these are valid only for uniform acceleration.
最常见的错误之一是没能为所有矢量设定统一的正方向。一旦选定了正方向，所有矢量（位移、速度、加速度）就必须遵守这个规定。对于竖直上抛运动，若设定向上为正却又使用 a = +g，就是典型错误。务必在开始计算前写下正方向约定。另一个陷阱是在加速度不恒定时仍然使用SUVAT方程——这些方程只适用于匀变速运动。
nder v-t = displacement, area under a-t = change in velocity. Always check units: displacement in metres, time in seconds, velocity in m s⁻¹, acceleration in m s⁻². Finally, when using the equation s = ut + ½ at², ensure you square the entire time t, not just half of it. Practise a wide range of past-paper questions, paying attention to how marks are allocated for setting up equations, substitution, and final answers with correct units.
在运动图像题中，学生经常混淆斜率和面积。请记牢：d-t图的斜率 = 速度，v-t图的斜率 = 加速度；v-t图下的面积 = 位移，a-t图下的面积 = 速度变化。一定要检查单位：位移用米，时间用秒，速度用 m s⁻¹，加速度用 m s⁻²。最后，使用 s = ut + ½ at² 时，注意是对整个时间 t 进行平方，而非只平方其一半。大量练习往年真题，注意题目如何为列出方程、代入数据和带有正确单位的最终答案分配分数。
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