CAIE IGCSE物理 运动 速度 加速度 图像
0625 的 1.2 Motion 是整份考纲里第一块运动学内容，Core 八条加 Supplement 五条，选择题卷和理论卷都会出。这一块的公式只有几个，真正拉开差距的是读图：距离时间图的斜率、速度时间图的面积、两根坐标轴的单位，任何一处读错，后面的计算再准也拿不到分。Cambridge 官方 March 2026 Principal Examiner Report 里，这类题的失分集中在把最高速度当成全程平均速度，或者干脆用速度乘时间代替面积。下面按考纲条目拆开讲，每一块给一条能直接用在卷面上的口径。
Topic 1.2 Motion carries the first block of kinematics in 0625, and it turns up in the multiple-choice paper as well as in the theory paper. The formulas are few; the marks go on graphs, where the gradient of a distance-time graph, the area under a speed-time graph and the units on both axes have to be settled before any calculation begins. The Principal Examiner Report for March 2026 records the same two errors every session, taking the maximum speed as the average speed of the whole journey and replacing an area with speed multiplied by time.
0625 三张卷里 1.2 运动的位置与分值
0625 的 Topic 1.2 Motion 落在 General physics，Core 有八条要求，Supplement 再加五条，Extended 考生两套都要掌握。这份 syllabus 是版本 1，2023 年 9 月发布，适用 2026、2027 与 2028 年考试，官方注明没有影响教学的重大变化。Core 考生考 Paper 1 与 Paper 3，成绩落在 C 到 G；Extended 考生考 Paper 2 与 Paper 4，可以拿到 A* 到 G。选择题卷 45 分钟 40 分占 30%，理论卷 1 小时 15 分钟 80 分占 50%，实验卷 Paper 5 一个半小时或者 Paper 6 一小时，都是 40 分占 20%。整科的评价目标按 AO1 五成、AO2 三成、AO3 两成分配，Paper 1 与 Paper 2 内部是 AO1 六成三、AO2 三成七，所以运动学的题大多考定义和公式有没有用对。Core 第 8 条单独给出 g 近似为 9.8 m/s^2，题目写了 10 就按 10 算。学生最常把三张卷的分工记混，拿实验卷的读数要求去准备理论卷。
Motion sits inside Topic 1 of 0625, where the Core content lists eight requirements and the Supplement adds five more for Extended candidates. The syllabus is version 1, published in September 2023 and valid for exams in 2026, 2027 and 2028, with no significant changes to teaching flagged by Cambridge. Core candidates sit Paper 1 and Paper 3 for grades C to G, while Extended candidates sit Paper 2 and Paper 4 for grades A* to G; the multiple-choice paper runs 45 minutes for 40 marks and 30% of the total, the theory paper 1 hour 15 minutes for 80 marks and 50%, and the practical paper 40 marks for 20%. Papers 1 and 2 divide their objectives as 63% AO1 and 37% AO2, so many kinematics items turn on whether a definition or an equation was applied exactly as written.
速度的定义与两个几乎一样的公式
Core 第 1 条把 speed 定义成 distance travelled per unit time，公式 v = s / t，单位是米每秒。第 3 条另给 average speed = total distance travelled / total time taken，两条公式在卷面上长得几乎一样，区别在于题目给的是完整路程还是位移。例：一名学生沿跑道跑 400 m 用了 80 s，平均速率是 400 / 80 = 5.0 m/s；如果他跑完一圈回到起点，平均速度是零，位移为零而路程是 400 m。单位换算只需要背一个数：1 m/s 等于 3.6 km/h，所以 20 m/s 就是 72 km/h，90 km/h 除以 3.6 得 25 m/s。1.2 的题目经常混着给单位，距离写 km 而时间是 min，动手前先把 km 换成 m 或把 min 换成 s，免得算出 km/min 却在答案里写 m/s。常见的错误是直接相除，答案的量纲错了以后数值再接近也不给分。阅卷时单位写错通常就丢掉那一分。
Core requirement 1 defines speed as distance travelled per unit time and gives v = s / t, while requirement 3 adds average speed as total distance travelled divided by total time taken. The two look identical on the page and separate cleanly once you ask whether the question supplies a whole path or a displacement; a runner covering 400 m of track in 80 s has an average speed of 5.0 m/s, and the same runner finishing back where they started has an average velocity of zero. Only one conversion is worth memorising, since 1 m/s equals 3.6 km/h, which makes 20 m/s the same as 72 km/h and 90 km/h the same as 25 m/s; mixing kilometres with minutes and then labelling the result m/s is the mistake markers see most often.
速率与速度 方向这一条怎么考
Core 第 2 条要求写出 velocity as speed in a given direction，Supplement 第 9 条把加速度定义成 change in velocity per unit time，两条前后咬合。方向在这里不是装饰，一个物体沿圆周以恒定速率运动时速率没变而速度一直在变，所以它有加速度。0625 的选择题喜欢这么问：小球绕圈时哪一个量保持不变，答案是速率而不是速度。写答案时留意 distance 与 speed 是标量，displacement 与 velocity 是矢量，用词对不上就丢分。跑道的例子最能说明差别，跑完一圈路程 400 m、位移为零，速率不为零、速度则为零。题目问 velocity 时只写一个数值、不写方向，那一分通常不给。很多学生以为方向只是文字要求，其实它决定了后面 Δv 该怎么算。
Requirement 2 defines velocity as speed in a given direction, and the Supplement builds on that by defining acceleration as the change in velocity per unit time. Direction is not decoration here, because an object moving round a circle at constant speed is still accelerating, which is why a multiple-choice item asks which quantity stays unchanged during circular motion. Distance and speed are scalars while displacement and velocity are vectors, and an answer that offers a number without a direction loses its mark whenever the question uses the word velocity.
距离时间图 斜率就是速度
距离时间图的斜率就是速率，Core 第 6 条要求用直线段上两点的坐标相减算斜率。图形语言只有三种：水平线表示 at rest，向上倾斜的直线表示 moving with constant speed，弯曲的曲线表示速度在变，加速段向上弯、接近减速末段变平。最陡的地方速度最大，March 2026 的报告专门提到考生是靠这一点认出最高速度的。常见的错误是把距离轴上的最大值当成最高速度，距离是路程而速率是路程除以时间，两者的单位都不一样。取点时优先挑落在网格线上的坐标，读数最稳，报告里记下的正确做法正是选 B 与 C 两点。时间从分钟换成小时、或者把 km/min 的斜率换算成 km/h，两种做法都可以，最终单位写清楚就行。图上没有印单位时，答案必须自己带上单位。
The gradient of a distance-time graph is the speed, and Core requirement 6 asks for that gradient to be taken from two points on a straight section. Only three shapes matter: a horizontal line is an object at rest, a rising straight line is constant speed, and a curve means the speed is changing, bending upwards while accelerating and flattening out as the object slows. The steepest point marks the maximum speed, which the March 2026 report confirms as the intended reading; a common slip is to take the largest distance value on the axis as the maximum speed, even though distance and speed are measured in different units. Coordinates sitting on grid lines give the steadiest readings.
速度时间图 斜率给加速度 面积给距离
速度时间图上有两种信息，斜率给加速度，线下面积给距离。Core 第 7 条写明面积法适用于匀速或匀加速两种情形，线段水平时面积是长方形，线段倾斜时面积是三角形或梯形。例：前 4.0 s 匀加速到 8.0 m/s，面积是 0.5 × 4.0 × 8.0 = 16 m；随后 5.0 s 保持 6.0 m/s，面积是 5.0 × 6.0 = 30 m，两段相加得 46 m。曲线段不能用 0.5 × 底 × 高，因为加速度一直在变，这也是报告里 non-linear acceleration 那一段容易被误判的原因。学生最常把速度时间图当距离时间图来读，直接把纵轴上的读数说成距离。Core 第 5 条要求从图形判断 at rest、constant speed、accelerating、decelerating 四种状态，依据只有斜率的正负与陡缓。图形题的答案先写形状、再写物理量、最后给数值，三层写全分就到手。
A speed-time graph carries two readings at once, with the gradient giving acceleration and the area below the line giving distance travelled. Core requirement 7 restricts the area method to constant speed or constant acceleration, so a horizontal line yields a rectangle while a sloping straight line yields a triangle or a trapezium; accelerating uniformly to 8.0 m/s in 4.0 s covers 16 m, and holding 6.0 m/s for the following 5.0 s covers 30 m, giving 46 m in total. Curved sections cannot be handled with half base times height because the acceleration keeps changing, which is the region the report flags as misread. The four states in requirement 5, at rest, constant speed, accelerating and decelerating, are all settled by the sign and the steepness of the gradient.
平均速度 瞬时速度与最高速度的差别
平均速度用整段路程除以整段时间，瞬时速度属于某一刻，March 2026 的报告点名的一道题就是把两者混起来。题目给一张全程 40 min 的旅行图，问全程平均速度，很多考生把图上最高点的读数直接抄成答案，或者用最高速度乘总时间。稳妥的做法是先读最高速度拿到瞬时值，再回到起点与终点的坐标算平均值，这道题里两个数值差得很明显。Core 第 3 条只要求 average speed 的定义，瞬时速度属于 Supplement 的理解范围，所以 Core 卷面上很少直接考。写答案时把算式列出来，数值算错也还能留下方法分。阅卷时看到卷面上只有一个孤立数值，通常先扣方法分再看答案。
Average speed divides the whole journey by the whole time, while instantaneous speed belongs to a single moment, and the March 2026 report names a question where the two were mixed up. Candidates read the highest point on a 40 minute journey graph and offered it as the average, or multiplied that top speed by the total time; the reliable route reads the peak for the instantaneous value and then returns to the start and end coordinates before dividing. Only the definition of average speed is required at Core, which is why instantaneous values appear mostly in Extended items.
加速度 a = Δv / Δt 与减速的符号
Supplement 第 9 条把加速度定义成 change in velocity per unit time，写法 a = Δv / Δt；第 11 条要求从速度时间图的斜率求出加速度，第 12 条说明 deceleration 就是负的加速度。例：汽车 6.0 s 内从静止加到 30 m/s，加速度是 (30 - 0) / 6.0 = 5.0 m/s^2；同一辆车 8.0 s 内从 24 m/s 停下，加速度是 (0 - 24) / 8.0 = -3.0 m/s^2，写成 deceleration 3.0 m/s^2 同样正确。符号是这里唯一的陷阱，题目问 deceleration 时答案里出现负号会被判错，问 acceleration 时反过来必须带负号。学生最常把 Δv 写成初速减末速，方向颠倒之后整题都跟着错。这一步最容易在选择题里丢分，因为选项里通常同时摆着 +3.0 与 -3.0 两个数。把末速写在前面、再减去初速，这个顺序默写一遍就不会乱。
The Supplement defines acceleration as the change in velocity per unit time, written as delta v divided by delta t, and adds that reading it from the gradient of a speed-time graph is expected, with deceleration treated as negative acceleration. A car reaching 30 m/s from rest in 6.0 s accelerates at 5.0 m/s^2, and the same car stopping from 24 m/s in 8.0 s has an acceleration of -3.0 m/s^2, which is equally correct when written as a deceleration of 3.0 m/s^2. The sign decides the mark, because a question asking for a deceleration rejects the negative value while one asking for acceleration requires it.
图表题的单位换算与时间区间
报告里的另一处失分是用单点求速度：考生把 v = s / t 套到图上的某一个坐标上，算出一个数就当答案交上去，正确做法是取两点坐标相减，分子分母都要用差值。时间轴同样按区间算，报告里一道小车题的正确时间段是 (5.0 - 2.0) = 3.0 s，很多考生直接取 5.0 s，面积因此偏大。那道题的标准答案是 6.0 m，来自两段面积相加。距离题与加速度题在图上长得像，报告专门指出有人把面积当成算加速度的途径。读图时先在草稿上写下两根轴的单位，再看题目问的是距离还是加速度，这两行字只要十几秒。错得最多的是把面积与斜率对调，写答案前回头看一眼纵轴写的是什么量。
A second pattern in the report is the use of a single coordinate, where candidates substitute one point from the graph into v = s / t and offer the result, when the correct move is to subtract two pairs of coordinates so that both the distance and the time are intervals. The same logic governs the time axis, where one trolley question expects an interval of 3.0 s from 5.0 s minus 2.0 s, and the standard answer of 6.0 m comes from adding the two areas. Many candidates used 5.0 s on its own and produced an area that was far too large.
自由落体与 g 取 9.8 还是 10
Core 第 8 条把 g 定成地球表面附近近似恒定的 9.8 m/s^2，考纲同时说明题目给了 10 就按 10 算。真空中的自由落体是匀加速运动，从静止释放后 2.0 s 末的速度是 9.8 × 2.0 = 19.6 m/s，这两秒内下落的距离是 0.5 × 9.8 × 2.0^2 = 19.6 m。数字相同只是巧合，要紧的是两条前提：初速为零、加速度恒为 g。g 的单位写 m/s^2 或 N/kg 都可以，因为 gravitational field strength 与自由落体加速度的数值一样。常见的错误是把 g 乘上时间以后当成距离交上去，两个数的量纲完全不同。阅卷时这类把速度当距离的答案通常算方法错，后面几问也连带拿不到分。
Requirement 8 states that g near the Earth's surface is approximately constant at 9.8 m/s^2, and the syllabus notes that a value of 10 may be used when a question supplies it. Free fall in a vacuum is uniformly accelerated, so an object released from rest reaches 19.6 m/s after 2.0 s and falls about 19.6 m in that time. Two conditions do the work here, an initial velocity of zero and an acceleration fixed at g; treating the product of g and time as a distance is the error that costs the whole item.
终端速度的四段下落过程
Supplement 第 13 条要求描述物体在均匀重力场中下落、有阻力和没有阻力两种情形，并写出 terminal velocity。过程分四段：刚释放时速度很小、空气阻力也很小，合力接近重力，加速度最大；速度增大后阻力增大，合力减小，加速度随之减小；阻力增大到与重力相等时合力为零，速度不再变化，这一段就是终端速度；换成液体过程一样，只是阻力更大、终端速度更低。很多学生以为到了终端速度物体就静止，其实它一直在匀速下落。空气阻力随速度增大而增大，这一句是解释加速度逐渐减小的关键，漏掉它一般拿不到完整分。题目要求解释时，把合力为零与速度恒定两句话都写出来，实验卷的口头描述题同样按这个顺序说。
The Supplement asks for the motion of a falling object to be described with and without air or liquid resistance, and for terminal velocity to be identified. Four stages run in order: the object leaves rest with small drag and a large net force, so acceleration is greatest; as speed rises the drag grows and both the net force and the acceleration fall; when drag matches weight the net force becomes zero and the speed stops changing, which is terminal velocity; and the same sequence happens in a liquid at a lower terminal speed. Terminal velocity does not mean the object is at rest, and answers that leave out the growth of drag rarely earn the explanation mark.
March 2026 报告里的五处失分
Cambridge 官方 March 2026 Principal Examiner Report 里与 1.2 直接相关的失分有五处：选择题里用最高速度代替面积求距离，把速度时间图与距离时间图的区域搞混，用 v = s / t 对单点求值，min 换 h 的步骤漏掉或把 km/min 直接写成 km/h，以及把 acceleration 与 deceleration 互相认错。报告还记了一处细节，考生回答图形区域时给出数值而不是语言描述，而这类题要的是文字说明。写图形题按三层组织：先写线段本身的变化，再写它代表的物理量，最后给数值与单位。阅卷时看的就是这三层有没有写全，答案的分落在哪一层一目了然。复习时把这几处失分抄成一页贴在书桌前，考前十分钟扫一遍就够。
The March 2026 report lists a handful of losses tied directly to this topic: taking the maximum speed instead of the area when a distance is wanted, mixing up regions of a speed-time graph with those of a distance-time graph, substituting a single point into v = s / t, mishandling the conversion between minutes and hours, and treating acceleration and deceleration as interchangeable. It also notes that some candidates answered graph questions with numbers when a written description was required. Structuring an answer as the shape of the line, the quantity it represents, and finally the value with its unit covers the three layers markers look for.
三周复习安排 读图 计算 错题归档
第一周只读图，从最近三份真题里挑出五道距离时间图和五道速度时间图，逐题写下两根轴的单位、斜率的含义、面积的含义，先不动笔算数。第二周进入计算，每道图都要求写出两点坐标相减的过程，距离题与加速度题各做十道，另外把 km/h 与 m/s 的互换单独练一页，练到不用想。第三周的整卷练习之后把错题按读图错、单位错、公式错三类归档，先看读图错那一类，这一类补起来最快。每周留一次二十分钟的口头复述，把终端速度那四段讲给同学听，讲不顺的地方就是还没记住的地方。g 取 9.8 还是 10、单位写 m/s^2 还是 N/kg，这两处在最后一晚再核对一次，考场上按题目给的数据用就行。
A three week plan splits cleanly. Week one is reading only, taking five distance-time and five speed-time graphs from recent papers and writing down the axis units, what the gradient means and what the area means, without calculating anything. Week two adds numbers, always through two pairs of coordinates, with separate practice on converting between km/h and m/s until it needs no thought. Week three is full papers and an error book sorted into reading errors, unit errors and formula errors, with the reading group reviewed first because it closes fastest.
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