CAIE物理 速度 加速度 图像 自由落体 备考
剑桥 IGCSE 物理 0625 的第一章叫「运动、力与能量」，运动学排在 1.2。这一节的知识点看着不多，题目密度却很高：Paper 1 与 Paper 2 的选择题里，读图题几乎每回都出现，Paper 3 与 Paper 4 的结构题又把速度、加速度、路程串在一道题里算。很多学生以为运动学就是背三个公式，真正丢分的地方往往在读轴与换单位。下面十二个小节按 0625 考纲 1.2 的条目顺序展开，属于补充内容的地方会标出来。
Cambridge IGCSE Physics 0625 opens with Topic 1, Motion, forces and energy, and motion sits at 1.2. The content looks small, but the questions are dense. Graph reading appears in Papers 1 and 2 almost every series, and Papers 3 and 4 keep linking speed, acceleration and distance inside one structured question. Most students treat motion as three formulas to memorise, while the marks usually go missing in reading the axes and converting units. The twelve short sections below follow the order of syllabus 1.2, with Supplement content flagged where it matters.
速度的定义与单位换算
考纲把速度定义为每单位时间走过的路程，公式写成 v = s / t，单位是米每秒。这条式子在 Core 只要求正用与反用：给出路程与时间求速度，或者给出速度与时间求路程。题目更愿意给公里每小时，换算是这一步最容易出问题的地方：1 km/h 就是 1000 米除以 3600 秒，所以 72 km/h 要先除以 3.6 得到 20 m/s，再代入公式，反向换算就乘 3.6。另一个常被忽略的点是平均速度用总路程除以总时间，中途停下休息的时间也算进总时间，不能只挑运动的那一段。上面这些条目在 Cambridge International 官网 0625 考纲 1.2 里可以逐条对上。
The syllabus defines speed as the distance travelled per unit time, giving v = s / t with the unit metres per second. At Core level the equation is used in both directions: distance and time give speed, or speed and time give distance. Questions often quote km/h instead, and the conversion is where marks disappear first; since 1 km/h is 1000 metres divided by 3600 seconds, 72 km/h becomes 20 m/s once you divide by 3.6, and multiplying by 3.6 takes you back; average speed uses the total distance over the total time, and time spent stationary still counts towards that total, an omission examiners see every series.
速率与速度的区别
Core 第二条把速度定义为某方向上的速率，1.1 的补充内容又要求区分标量与矢量。路程、速率、时间、质量、能量、温度是标量，只有大小；力、重力、速度、加速度、动量、电场强度和重力场强度是矢量，既有大小也有方向。这条定义直接决定作答方式：题目问 velocity，方向就不能省，只写 15 m/s 会丢分，要写成 15 m/s 向北这样的完整表述。汽车绕弯时速度大小没变，方向一直在变，所以速度仍然在变。阅卷时经常看到学生把 speed 与 velocity 当成同一个词，中英文混写时尤其容易乱。
Core content defines velocity as speed in a given direction, while the Supplement to 1.1 asks for the scalar and vector split. Distance, speed, time, mass, energy and temperature carry magnitude only; force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength carry direction as well. That definition decides how you answer, because a question asking for velocity loses the mark when the direction is dropped, so write 15 m/s due north rather than 15 m/s alone; a car rounding a bend at a steady speed is still changing velocity, since its direction keeps changing; treating the two words as interchangeable is a common English-medium slip.
位移时间图像的斜率就是速度
位移时间图像的纵轴是路程，横轴是时间。直线段的斜率就是速度，做法是取相隔较远的两点，用路程的变化量除以时间的变化量。水平线表示物体静止，路程不再随时间变化。图形越陡速度越大，比较两段快慢时把陡这个字写进理由就够了。举一个可以核对的例子：一条线在 300 秒内上升 1500 米，斜率是 5 m/s。常见的错误是没先看纵轴单位是米还是千米，把千米直接当米除以秒，数量级立刻差一千倍。考纲要求 plot 与 sketch 都会，画图时两条轴都要标出物理量与单位。
A distance-time graph puts distance on the vertical axis and time on the horizontal, and the gradient of a straight section is the speed. Take two well-separated points on the line and divide the change in distance by the change in time. A horizontal line means the object is at rest, because the distance stops changing, while a steeper line means a faster object, and steepest gradient is the reason to give when two sections are compared. One checkable case: a line rising 1500 m in 300 s shows a constant 5 m/s. The recurring error is reading an axis marked in kilometres as metres, which throws the answer out by a factor of a thousand; labelled axes with units are part of the sketching requirement.
曲线段与切线求瞬时速度
位移时间图像出现曲线时，速度正在变化。曲线越来越陡表示加速，越来越平表示减速。要求某一时刻的瞬时速度，就在那一点画切线，切线只接触不穿过曲线，再在切线上取一个足够大的三角形算斜率，三角形取小了读数误差会被放大。很多学生以为曲线段也能像直线段那样整段求斜率，那样得到的是整段的平均速度，不是题目问的那个时刻。考纲对这条只要求定性判断，所以草图题按形状给分，数值不是重点。
When the line on a distance-time graph curves, the speed is changing: a curve getting steeper means accelerating, and a curve flattening out means decelerating. To find the speed at one moment, draw a tangent that touches but does not cross the curve at that point, then use a large triangle on the tangent to work out its gradient, since a small triangle magnifies any reading error. The usual mistake is treating a whole curved section as one slope, which returns an average rather than the value at the instant asked for; the syllabus asks for this qualitatively, so a sketch is marked on shape rather than on measured numbers.
加速度的定义与单位
补充内容把加速度定义为速度的变化量与所用时间的比，公式是 a = Δv / Δt，单位 m/s²。变化量等于末速度减初速度，符号不能改：减速时末速度小于初速度，变化量是负的。加速度 2 m/s² 的含义是每秒钟速度增加 2 m/s，这句表述比符号形式更常被考。题目给出一辆汽车 4 秒内从 5 m/s 加到 25 m/s，变化量是 20 m/s，除以 4 s 得到 5 m/s²。若问的是时间或末速度，把这条公式变形即可，不必再背第二组公式。
The Supplement defines acceleration as the change in velocity per unit time, written a = Δv / Δt with the unit m/s². Change in velocity means final velocity minus initial velocity, and the sign has to be kept, because a slowing object has a smaller final value and therefore a negative change. An acceleration of 2 m/s² means the velocity grows by 2 m/s every second, and that sentence is examined more often than the symbol form; if a car goes from 5 m/s to 25 m/s in 4 s, the change is 20 m/s and the answer is 5 m/s²; questions asking for the time or the final velocity are answered by rearranging this one equation.
速度时间图像的斜率是加速度
速度时间图像把速度放在纵轴。直线段的斜率就是加速度，向上倾斜是加速，向下倾斜是减速。贴着时间轴的水平线表示静止，轴上方的水平线表示匀速运动，此时加速度为零。判断加速度大小看陡峭程度，两段比较就把斜率更陡写进理由。考纲还要求能从数据判断，表格题里每两秒速度增加相同的量，同样说明是恒定加速度。作答时先写公式再代数，中间不要省掉单位。
On a speed-time graph the speed sits on the vertical axis, and the gradient of a straight section is the acceleration: sloping up means accelerating and sloping down means decelerating. A horizontal line along the time axis is an object at rest, while a horizontal line above it is motion at constant speed with zero acceleration. Compare accelerations by how steep each line is, and give steeper gradient as the reason. The syllabus also asks for this judgement to be made from data, so equal speed rises over equal time intervals in a table mean constant acceleration; show the equation before substituting numbers, and keep units attached throughout.
图像下方的面积就是路程
速度时间图像下方的面积就是路程，这条规则对匀速与恒定加速度的运动都成立。面积按矩形、三角形或梯形分别计算：匀速段是矩形，从静止起步的加速段是三角形，速度从 u 变到 v 的加速段是梯形，面积等于 u 加 v 再除以 2 乘时间。举个例子：0 到 20 m/s 用 4 秒，面积 40 米；接着 20 m/s 匀速 6 秒，面积 120 米；最后 5 秒停下，面积 50 米，合计 210 米。最容易错的是只算加速段，或者忘记最后一段也要计入。时间轴单位若是分钟，先换成秒再算面积。
The area under a speed-time graph is the distance travelled, and the rule holds for constant speed and constant acceleration alike. Split that area into rectangles, triangles or a trapezium: a constant-speed section is a rectangle, an acceleration from rest is a triangle, and a section running from u to v is a trapezium whose area is u plus v, divided by 2 and multiplied by the time. One worked case: 0 to 20 m/s in 4 s gives 40 m, a steady 20 m/s for 6 s adds 120 m, and stopping in 5 s adds 50 m, a total of 210 m; students most often compute only the acceleration phase or leave the final phase out; if the time axis is in minutes, convert to seconds before finding any area.
减速就是负的加速度
减速在图形上的斜率向下，数值上是负的加速度。作答有两种写法都可以：写加速度为负 1.5 m/s²，或者写出大小并说明这是 1.5 m/s² 的减速。常见的错误是把减速理解成加速度在变小，这两件事并不相同：匀减速时加速度大小恒定，只是方向与运动方向相反。另一种失分是丢掉负号只写大小，题目若问 acceleration，符号本身就是答案的一部分。速度从 12 m/s 在 8 秒内减到零，变化量是负 12 m/s，除以 8 秒得到负 1.5 m/s²。
Deceleration appears as a downward gradient and is a negative acceleration. Either answer form is accepted: quote the acceleration as negative 1.5 m/s², or give the size and call it a deceleration of 1.5 m/s². The persistent misconception is to read deceleration as an acceleration that is getting smaller, which is a different idea, because in uniform deceleration the magnitude stays constant while the direction opposes the motion; dropping the minus sign when the question asks for the acceleration costs part of the mark; take a speed falling from 12 m/s to zero in 8 s: the change is negative 12 m/s, so the value is negative 1.5 m/s².
恒定加速度与变化加速度
补充内容要求在数据与图形之间判断恒定加速度与变化加速度。直线斜率不变就是恒定加速度；曲线表示加速度本身在变，曲线变平说明加速度在减小，曲线变陡说明加速度在增大。表格数据里每段相等时间速度增加相同的量，判为恒定加速度；每次读数都一样则判为匀速。画草图时先用标签标明两条轴，再按描述落下形状，直线段用尺子，曲线段弯得自然。这一步最容易在草图题上丢分，因为形状对了才有分，数值并不重要。
The Supplement asks you to tell constant acceleration from changing acceleration, both from data and from the shape of a graph. A straight sloping line means the gradient, and therefore the acceleration, is the same everywhere; a curve means the acceleration itself is changing, flattening when it decreases and steepening when it increases. In a table, equal speed rises over equal time intervals mean constant acceleration, while an unchanged speed means constant speed; when sketching, label both axes first and then follow the description, drawing straight sections with a ruler and curves smoothly; shape carries the marks, not the numbers.
自由落体与 g 的取值
Core 要求说明地球表面附近自由落体的加速度近似恒定，取约 9.8 m/s²，这个值不随物体质量改变，重的石头与一张纸在忽略空气阻力时下落一样快。算下落速度用 v = u + at，从静止释放时 u 等于零，下落 2 秒的速度是 9.8 乘 2 得 19.6 m/s。下落高度用面积法更快，速度随时间直线升到 19.6 m/s，三角形面积是 0.5 乘 2 乘 19.6，约 20 米。题目允许用 10 m/s² 时通常会在题干写明，没写就按 9.8 算。结果保留的位数要跟题干给的数据一致，多写的位不加分。
Core content states that the acceleration of free fall near the Earth's surface is approximately constant at about 9.8 m/s², and the value does not depend on mass, so a heavy stone and a sheet of paper fall at the same rate once air resistance is ignored. Use v = u + at with u equal to zero for a release from rest, which gives 19.6 m/s after 2 s. The distance fallen comes faster from the graph area, since the speed rises linearly to 19.6 m/s and the triangle gives 0.5 × 2 × 19.6, about 20 m; a question that intends 10 m/s² says so in the stem, so use 9.8 otherwise, and match the significant figures to the data given because extra digits earn nothing.
空气阻力与终端速度
真实的下落里存在空气阻力，考纲在力的部分把它算作摩擦的一种，阻力随下落速度增大而增大。合力减到零时物体不再加速，速度停在最大值，这个状态叫终端速度。速度时间图像画出来是一条先陡后平的曲线：前半段阻力小、合力向下，加速快；后半段斜率越来越小，说明加速度在减小，最终斜率变为零。跳伞的例子常被用来考第二段，伞打开后阻力变大，合力向上，速度先迅速下降，再落到一个更小的新终端速度。作图题把这条曲线画成先弯后平就对了，不要画成直线。
Real falls include air resistance, which the syllabus treats as a form of friction and which grows as the speed increases. When the resultant force falls to zero the object stops accelerating and settles at its maximum speed, the terminal velocity. Plotted on a speed-time graph this is a curve that rises steeply and then flattens: early on, drag is small and the resultant force points downwards, so the acceleration is large, and later the gradient shrinks until it reaches zero; a parachute opening makes a second phase worth describing, because the extra drag briefly makes the resultant force point upwards and the object settles at a lower terminal velocity; draw the shape as a curve that levels off, never as a straight line.
三卷结构与备考优先级
0625 的考纲适用于 2026 至 2028 年的考试，Cambridge International 官网在 2025 年 12 月发布了第二版，那一版只更新了第 56 页的一个网页链接，考点与卷面结构没有变化。所有考生考三份卷子：Paper 1 或 Paper 2 是四选一选择题，45 分钟 40 分，占 30%；Paper 3 或 Paper 4 是结构题，1 小时 15 分钟 80 分，占 50%；Paper 5 是实验操作卷 1 小时 15 分钟，Paper 6 是实验笔试卷 1 小时，都是 40 分、占 20%。选 Core 卷最高拿到 C 等，选 Extended 卷覆盖 Core 与补充内容，可拿 A* 到 G。评分目标里知识理解占 50%，信息处理与解题占 30%，实验技能占 20%，运动学的计算题正好落在前两项之间。
The 0625 syllabus covers examinations in 2026, 2027 and 2028, and Cambridge International published version 2 in December 2025 with a single change, an updated weblink on page 56, so the content and the paper structure stand as before; every candidate sits three papers: Paper 1 or Paper 2 is four-option multiple choice, 45 minutes for 40 marks and 30 per cent of the total; Paper 3 or Paper 4 is structured theory, 1 hour 15 minutes for 80 marks and 50 per cent; and Paper 5, the 1 hour 15 minute practical test, or Paper 6, the 1 hour alternative to practical, carries 40 marks and 20 per cent. Core papers cap the available grade at C, while the Extended route covers Core and Supplement content and reaches A*; the assessment objectives place 50 per cent on knowledge with understanding, 30 per cent on handling information and problem-solving and 20 per cent on experimental skills, and motion calculations sit between the first two.
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