AS Physics: Kinematics — Essential Revision Guide | AS 物理：运动学考点精讲

📚 AS Physics: Kinematics — Essential Revision Guide | AS 物理：运动学考点精讲

Kinematics is the branch of mechanics that describes the motion of objects without considering the causes of that motion. For AS-level Physics, mastering definitions of displacement, velocity, and acceleration, along with the equations of motion for constant acceleration, forms the foundation for tackling both theoretical and practical problems. This revision guide walks you through every key concept, graph interpretation, and equation you need to excel.

运动学是力学的一个分支，它描述物体的运动而不考虑导致运动的原因。对于 AS 物理而言，掌握位移、速度、加速度的定义，以及匀加速运动方程，是解决理论和实际问题的基石。本复习指南将带你逐一攻克每一个关键概念、图像解读和必考方程，助你取得优异成绩。

1. Scalar and Vector Quantities | 标量与矢量

In kinematics, it is crucial to distinguish between scalar quantities, which have magnitude only, and vector quantities, which have both magnitude and direction. Distance and speed are scalars; displacement and velocity are vectors. Understanding this difference prevents sign errors when applying equations of motion, especially when objects change direction.

在运动学中，区分只有大小的标量和既有大小又有方向的矢量至关重要。距离和速率是标量，而位移和速度是矢量。理解这一区别可以避免在应用运动方程时出现符号错误，尤其是在物体改变方向的情况下。

For example, if a runner completes one full lap of a 400 m track, the distance travelled is 400 m, but the displacement is 0 m because the start and end points coincide. Average speed would be total distance ÷ time, whereas average velocity would be zero. In one-dimensional motion, we often assign a positive direction (e.g., right or up) and treat opposite directions as negative.

例如，如果一名运动员跑完一圈 400 米的跑道，他所经过的路程是 400 米，但位移为 0 米，因为起点和终点重合。平均速率等于总路程除以时间，而平均速度则为零。在一维运动中，我们通常规定一个正方向（如向右或向上），并将相反方向视为负向。

Distance (scalar): total length of path travelled, always positive.
Displacement (vector): straight-line distance in a given direction from start to finish.
Speed (scalar): rate of change of distance; average speed = total distance / total time.
Velocity (vector): rate of change of displacement; average velocity = Δdisplacement / Δtime.

路程（标量）：运动路径的总长度，恒为正值。
位移（矢量）：从起点到终点的有向直线距离。
速率（标量）：路程的变化率；平均速率 = 总路程 / 总时间。
速度（矢量）：位移的变化率；平均速度 = 位移变化量 / 时间变化量。

2. Acceleration and Its Direction | 加速度及其方向

Acceleration is defined as the rate of change of velocity; it is a vector quantity. An object accelerates if its speed changes, its direction changes, or both. In AS Physics, we primarily deal with constant acceleration in a straight line, but it is important to recognise that a negative acceleration (often called deceleration) means the acceleration vector points opposite to the velocity vector, causing the object to slow down.

加速度定义为速度的变化率，是一个矢量。如果物体的速率改变、方向改变或者两者同时改变，物体就在做加速运动。在 AS 物理中，我们主要处理直线上的匀加速运动，但需要认识到负加速度（常称为减速）意味着加速度矢量与速度矢量方向相反，从而导致物体减速。

If we define the upward direction as positive, a ball thrown vertically upward has a downward acceleration due to gravity of g ≈ 9.81 m s⁻², which is negative in this coordinate system. While the ball is moving upward, its velocity is positive and acceleration is negative, so it slows down. On the way down, velocity becomes negative, and acceleration is still negative, so its speed increases in the downward direction.

如果我们规定向上为正方向，竖直上抛的小球由于重力作用具有向下的加速度 g ≈ 9.81 m s⁻²，在此坐标系下为负。小球向上运动时，速度为正，加速度为负，因而减速；下降时速度变为负，加速度仍为负，因此向下的速度大小增加。

The standard unit of acceleration is m s⁻² (metres per second squared). The instantaneous acceleration can be found from the gradient of a velocity–time graph, a skill frequently tested in exams.

加速度的标准单位是米每二次方秒（m s⁻²）。瞬时加速度可以通过速度-时间图像的斜率求得，这是考试中经常考查的技能。

3. The SUVAT Equations of Motion | 运动学五大方程 (SUVAT)

For motion in a straight line with constant acceleration, five key equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). You must be able to select the correct equation based on which quantities are known and which is required.

对于匀加速直线运动，五个关键方程将位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t) 联系起来。你必须能够根据已知量和待求量选择合适的方程。

v = u + at

s = ut + ½at²

s = vt − ½at²

s = ½(u + v)t

v² = u² + 2as

These equations are valid only when acceleration is constant. If acceleration varies, you must use graphical methods or calculus (for further study). Remember to assign a consistent sign convention to all vector quantities.

这些方程仅在加速度恒定时成立。如果加速度变化，则必须使用图像法或微积分（后续学习内容）。务必对所有矢量规定一致的符号规则。

Equation	Missing quantity
v = u + at	s
s = ut + ½at²	v
s = vt − ½at²	u
s = ½(u + v)t	a
v² = u² + 2as	t

A common exam mistake is using the wrong equation for a situation where time is not given or not asked for; v² = u² + 2as often provides the quickest route in such cases.

一个常见的考试错误是，在没有给出或不需求解时间的情况下使用了错误的方程；此时 v² = u² + 2as 往往能提供最快捷的解题思路。

4. Free Fall and Acceleration Due to Gravity | 自由落体与重力加速度

An object falling freely near the Earth’s surface experiences a constant downward acceleration g = 9.81 m s⁻², provided air resistance is negligible. The same SUVAT equations apply, with a replaced by g (or −g depending on the chosen sign convention). Many AS problems involve objects dropped from rest, thrown vertically upward, or projected horizontally.

在地球表面附近，若空气阻力可忽略，自由下落的物体将受到恒定的向下加速度 g = 9.81 m s⁻²。同样的 SUVAT 方程仍然适用，只需将 a 替换为 g （或 −g，取决于符号规定）。许多 AS 物理题目涉及物体从静止下落、竖直上抛或水平抛出。

When an object is thrown upward, it momentarily stops at the highest point (v = 0), but its acceleration is still g downward. A typical question asks for the maximum height reached, which can be calculated using v² = u² + 2as with v = 0 and a = −g.

当一个物体被向上抛出时，它在最高点瞬间静止（v = 0），但其加速度仍然是向下的 g。典型的题目会要求计算上升的最大高度，可利用 v² = u² + 2as，令 v = 0 且 a = −g 来求解。

For an object dropped from rest, u = 0, so s = ½gt² and v = gt. This shows that displacement is proportional to the square of the time, a relationship often verified in laboratory experiments using a trapdoor mechanism or light gates.

对于从静止下落的物体，u = 0，因此 s = ½gt²，v = gt。这表明位移与时间的平方成正比，这一关系常在利用电磁铁和光电门的实验中进行验证。

5. Motion Graphs: Displacement–Time | 位移-时间图像

A displacement–time (s–t) graph plots displacement on the vertical axis against time on the horizontal axis. The gradient of the graph gives the instantaneous velocity. A straight line indicates constant velocity; a horizontal line indicates the object is stationary (zero velocity). A curve means the velocity is changing, i.e., acceleration is present.

位移-时间（s–t）图以纵轴表示位移，横轴表示时间。图像的斜率给出瞬时速度。一条直线表示匀速运动；水平线表示物体静止（速度为零）；一条曲线则表示速度在变化，即存在加速度。

If the curve becomes steeper over time, the velocity is increasing; if it flattens, the velocity is decreasing. The sign of the gradient gives the direction of motion: a positive gradient means the object is moving in the positive direction, while a negative gradient means it is moving in the negative direction. A turning point (maximum or minimum) represents a change in direction, where velocity is momentarily zero.

如果曲线随时间变得越来越陡，说明速度在增大；如果曲线趋于平缓，说明速度在减小。斜率的正负表示运动方向：正斜率表示物体向正方向运动，负斜率表示向负方向运动。图像的转折点（极大值或极小值）代表运动方向改变的时刻，此处速度瞬间为零。

AS exams might ask you to sketch an s–t graph for a given scenario, such as a ball thrown upward and caught again. The graph would start at s = 0, rise to a maximum, and return to s = 0, forming a symmetric parabola when air resistance is ignored.

AS 考试可能会要求你根据给定的情形绘制 s–t 图，例如上抛小球被接住的过程。如果不计空气阻力，图像将从 s = 0 开始，上升至最大值，然后回到 s = 0，形成一条对称的抛物线。

6. Motion Graphs: Velocity–Time | 速度-时间图像

The velocity–time (v–t) graph is one of the most powerful tools in kinematics. Its gradient gives acceleration, and the area under the graph (between the line and the time axis) gives the change in displacement. A horizontal line means constant velocity (zero acceleration); a sloping straight line indicates constant acceleration; a curve signals changing acceleration.

速度-时间（v–t）图像是运动学中最有力的工具之一。其斜率表示加速度，图线下与时间轴之间包围的面积表示位移的变化量。一条水平线表示匀速运动（加速度为零）；一条倾斜的直线表示匀加速运动；一条曲线则表示加速度在变化。

When the line crosses the time axis, the object changes direction. For example, a ball thrown upwards with initial positive velocity will have a velocity that decreases linearly, crosses the axis at the peak (v = 0), and becomes negative on the way down. The total area (treating areas below the axis as negative) gives the net displacement, while the sum of absolute areas gives the total distance travelled.

当图线穿过时间轴时，表示物体改变了运动方向。例如，以正初速度上抛的小球，其速度线性减小，在最高点处穿过时间轴（v = 0），下落时速度变为负值。总面积（时间轴下方的面积计为负值）给出净位移，而各面积绝对值之和给出总路程。

Exam questions frequently ask you to calculate acceleration from the gradient or distance from the area. It is vital to show clearly how you break the area into rectangles, triangles, or trapeziums and to state the formula used.

考试题目经常要求根据斜率计算加速度或根据面积计算路程。务必清晰地展示如何将面积分解为矩形、三角形或梯形，并写出所用公式。

7. Projectile Motion: Horizontal and Vertical Components | 抛体运动：水平与竖直分量

An object projected horizontally or at an angle follows a parabolic path under the influence of gravity, assuming negligible air resistance. The key to solving projectile problems is to treat the horizontal and vertical motions independently. Horizontally, velocity is constant (aₓ = 0). Vertically, acceleration is constant (aᵧ = −g).

在忽略空气阻力的情况下，水平抛出或以一定角度抛出的物体会在重力作用下沿抛物线路径运动。解决抛体问题的关键是独立分析水平方向和竖直方向的运动。水平方向上，速度恒定（aₓ = 0）；竖直方向上，加速度恒定（aᵧ = −g）。

The initial velocity vector can be resolved into horizontal and vertical components. For a projectile launched at an angle θ to the horizontal with speed u: uₓ = u cos θ, uᵧ = u sin θ. The time of flight is determined entirely by the vertical motion, usually by considering when the projectile returns to its original vertical level (sᵧ = 0) or hits the ground.

初速度矢量可以分解为水平和竖直分量。对于以速率 u 且与水平方向成 θ 角抛出的物体：uₓ = u cos θ，uᵧ = u sin θ。飞行时间完全由竖直运动决定，通常考虑物体返回初始竖直高度（sᵧ = 0）或落地时刻来求解。

For a projectile launched and landing on the same horizontal level, the time of flight T = (2u sin θ)/g, the maximum height H = (u² sin² θ)/(2g), and the horizontal range R = (u² sin 2θ)/g. These derived formulas are not always given on formula sheets, so understanding their origin from SUVAT is essential.

对于在同一水平面上发射并落地的抛体，飞行时间 T = (2u sin θ)/g，最大高度 H = (u² sin² θ)/(2g)，水平射程 R = (u² sin 2θ)/g。这些推导公式不一定会出现在公式表中，因此理解它们如何从 SUVAT 方程导出至关重要。

8. Terminal Velocity and Air Resistance | 终端速度与空气阻力

Although many AS kinematics problems assume no air resistance, you must also understand that in real fluids, drag forces increase with speed. An object falling through air or liquid initially accelerates due to gravity, but as speed increases, drag grows until it balances the weight. At this point, the net force is zero, acceleration becomes zero, and the object falls at a constant terminal velocity.

尽管许多 AS 运动学题目假设无空气阻力，但你仍需了解在真实流体中，阻力会随速度增大而增大。在空气或液体中下落的物体最初因重力而加速，但随着速度增加，阻力逐渐增大，直至与重力平衡。此时合力为零，加速度为零，物体以恒定的终端速度下落。

A velocity–time graph for a skydiver shows an initial steep increase in velocity, then a gradual levelling off to terminal velocity. When the parachute opens, the drag force suddenly increases, causing deceleration until a new, lower terminal velocity is reached. Being able to sketch and interpret such graphs demonstrates understanding of the link between forces and kinematics.

跳伞者的速度-时间图像显示速度起初急剧增加，然后逐渐趋于平稳达到终端速度。当降落伞打开时，阻力突然增大，导致减速，直至达到一个新的、较低的终端速度。能够绘制并解读此类图像，可以体现你对力与运动学之间联系的理解。

Exam questions might ask you to explain the shape of the graph in terms of forces, net force, and acceleration, combining kinematics with Newton’s second law. This is a classic synoptic skill.

考试题目可能会要求你用力、合力和加速度来解释图像形状，将运动学与牛顿第二定律结合起来，这是一种经典的综合性考查技能。

9. Experiments and Data Analysis Techniques | 实验与数据分析方法

Practical skills are assessed both in the laboratory and in written papers. A common AS experiment is measuring acceleration due to gravity using a free-fall apparatus. An electromagnet releases a steel ball, and the time taken to fall a known height is measured with a trapdoor switch or light gates. By varying the height and timing multiple falls, you can plot s against t² and find g from the gradient (since s = ½gt²).

实验技能既在实验室中考查，也在笔试中考查。一个常见的 AS 实验是使用自由落体装置测量重力加速度。电磁铁释放钢球，通过碰停开关或光电门测量下落已知高度所需的时间。通过改变高度并测量多次下落的时间，你可以绘制 s–t² 图，并由斜率求出 g（因为 s = ½gt²）。

Another classic investigation uses an air track with gliders to study constant velocity and constant acceleration (by tilting the track slightly). Motion sensors or ultrasound detectors can generate real-time displacement–time and velocity–time graphs, allowing students to compare theoretical predictions with experimental data. Understanding systematic and random errors, and calculating percentage difference, is vital for the analysis section.

另一个经典探究实验是使用气垫导轨和滑块来研究匀速运动和匀加速运动（通过略微倾斜导轨）。运动传感器或超声波探测器可以生成实时的位移-时间和速度-时间图像，让学生能够将理论预测与实验数据进行比较。理解系统误差和随机误差，并计算百分差，对分析部分至关重要。

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

Many students confuse displacement with distance, or velocity with speed, especially in “round trip” problems. Always check whether the question asks for displacement or distance, velocity or speed. Another pitfall is forgetting that the SUVAT equations only work for constant acceleration. If you’re given a v–t graph with a changing slope, you cannot simply plug numbers into an equation; you must use the graph.

许多学生将位移与路程、速度与速率混淆，尤其是在“往返”问题中。始终要确认题目问的是位移还是路程，速度还是速率。另一个易错点是忘记 SUVAT 方程仅适用于匀加速运动。如果给出的 v–t 图斜率变化，你不能简单地将数字代入方程，必须利用图像求解。

When dealing with projectiles, a common mistake is neglecting that horizontal and vertical motions are linked only by time. Solve for time using vertical information, then use that time to find horizontal displacement. Also, never forget to include units and express final answers to an appropriate number of significant figures, usually 2 or 3 unless otherwise stated.

处理抛体运动时，一个常见的错误是忽略水平与竖直运动仅通过时间联系在一起这一事实。利用竖直信息求解时间，再用该时间求水平位移。此外，永远不要忘记写上单位，并以适当的有效数字（通常 2 或 3 位）给出最终答案，除非题目另有说明。

Practice past paper questions regularly, especially those that combine graphs and equations. Drawing a quick sketch of the motion, labeling known quantities with their signs, and listing the five variables (s, u, v, a, t) before choosing an equation can dramatically reduce errors.

定期练习历年真题，尤其是那些将图像与方程结合的题目。在动笔前快速画出运动示意图，标出已知量和符号，并列出五个变量（s, u, v, a, t）再选方程，可以显著减少错误。

11. Vector Composition and Relative Velocity | 矢量合成与相对速度

In some AS syllabi, you may encounter relative velocity problems, such as finding the velocity of a boat crossing a river with a current. The resultant velocity is the vector sum of the boat’s velocity in still water and the river’s velocity. Similarly, for an aircraft affected by wind, the velocity relative to the ground is the vector addition of the aircraft’s airspeed and the wind velocity.

在某些 AS 大纲中，你可能会遇到相对速度问题，例如计算船在有水流的河中横渡的速度。合速度是船在静水中的速度与水流速度的矢量和。同样，对于受风影响的飞机，其相对地面的速度是飞机空速与风速的矢量相加。

You are expected to find the magnitude and direction of the resultant vector using Pythagoras’ theorem and trigonometry (sine, cosine, tangent) or by scale drawing. The parallelogram or tip-to-tail method is often used. Exam questions may also ask for the angle of drift or the time to cross, which depends only on the component of velocity perpendicular to the river banks.

你应能使用勾股定理和三角函数（sin、cos、tan）或比例绘图法求出合矢量的大小和方向。平行四边形法则或首尾相接法经常使用。考试题目还可能要求计算偏航角或渡河时间，后者仅取决于垂直于河岸的速度分量。

12. Summary and Key Formulae Checklist | 总结与关键公式清单

To excel in AS kinematics, you must internalise the definitions, recognise when constant acceleration applies, and fluently move between graphs, vector components, and SUVAT equations. Keep this checklist in your revision notes:

要在 AS 运动学中取得优异成绩，你必须内化各个定义，识别匀加速的条件，并在图像、矢量分量与 SUVAT 方程之间自如切换。请将下面的清单纳入你的复习笔记：

v = u + at
s = ut + ½at²
s = vt − ½at²
s = ½(u + v)t
v² = u² + 2as
g = 9.81 m s⁻² (downward)
Projectile horizontal: vₓ = u cos θ, aₓ = 0
Projectile vertical: vᵧ = u sin θ − gt, aᵧ = −g
Gradient of s–t graph = velocity
Gradient of v–t graph = acceleration; area = displacement

Consistent practice with a variety of problems, from simple drop-and-catch to multi-step projectiles, will build the confidence you need. Remember that drawing a diagram and writing down what you know (with signs) is half the solution.

通过反复练习各种题型，从简单的抛接问题到多步抛体运动，你将建立起所需的信心。请记住，画出示意图并写出已知量（包括符号）就已经解决了一半的问题。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

AS Physics: Kinematics — Essential Revision Guide | AS 物理：运动学 考点精讲