WJEC物理 速度 加速度 图像 停止距离 F=ma
WJEC 的 GCSE Physics 把运动学放在 Unit 2 里，考纲标题只有一句 Distance, speed and acceleration，翻开正文才发现里面装着图像、加速度与停止距离三块内容。很多学生以为这一节就是把 v = s / t 代进去算数，真正丢分的地方却在图像的斜率和面积上。这一篇按 WJEC 官网现行 specification 的第 25 至 26 页条目顺序，把 2.1 节连同紧邻的牛顿三定律拆开讲，每个知识点后面写清楚考场上常见的错误。文中出现的分值、卷面时长与分层规则取自考纲原文，停止距离的数字取自 gov.uk 的 Highway Code 页面。
WJEC's GCSE Physics puts kinematics inside Unit 2, under a heading that says only distance, speed and acceleration. Most revision guides treat the topic as a formula drill, yet the marks usually disappear on graph work, where the gradient and the area carry the physics. What follows keeps the arithmetic attached to the graph questions that carry it in the exam, and stays in the order of the current specification. Marks, timings and tier rules come from the WJEC specification; the stopping distances come from the Highway Code on gov.uk.
Unit 2 的分量与两份卷的分工
Unit 2 叫 FORCES, SPACE and RADIOACTIVITY，笔试 1 小时 45 分钟，80 分，占整个资格 45%。Unit 1 的时长、分值与占比完全相同，Unit 3 是实验考核，30 分只占 10%，由 WJEC 外部评卷，安排在一月底到二月的上半学期。运动学的重量因此不由它自己决定，它和天体、宇宙、放射性挤在同一张 80 分的卷子里。考试分两个层级，Higher 给 A* 到 D，Foundation 给 C 到 G。这门资格由 Qualifications Wales 监管，specification 封面明确写着不向英格兰的考点开放。WJEC 官网又挂出更新版考纲，从 2026 年 9 月起教授，其中 Unit 3 换成了新的设计，2.1 的运动学条目本身没有挪位置。
The written paper for Unit 2 lasts 1 hour 45 minutes and is worth 80 marks, which is 45 per cent of the qualification. Unit 1 carries exactly the same weight, while Unit 3 is a practical assessment of 30 marks worth 10 per cent, marked externally and taken between January and February. Kinematics therefore shares one paper with stars, the universe and radioactivity, and the qualification is regulated by Qualifications Wales and closed to centres in England. WJEC has also published an updated specification for first teaching in September 2026, which brings a new Unit 3 while leaving the motion content of 2.1 where it was.
speed 与 velocity：方向这一分不能省
speed 是标量，只回答快慢；velocity 是矢量，还要说清楚朝哪一边。考纲把这两个词写在同一行，答卷上却常常用错。很多学生以为算出 12 m/s 就算答完，题目问 velocity 时还得补方向，否则那一分拿不到。distance 与 displacement 的关系一模一样：绕操场跑一圈 400 m，distance 是 400 m，displacement 是 0。平均速度用总 distance 除总 time，不是把几个瞬时速度相加再取平均。上坡 6 m/s、下坡 10 m/s 走同一段路，平均速度是 7.5 m/s 而不是 8 m/s，因为慢的那一段占用的时间长。
Speed is a scalar and answers only how fast, whereas velocity is a vector and has to carry a direction. The specification lists both on the same line, and scripts still lose marks by giving a bare number when the question asks for velocity. Distance and displacement follow the same split, so one lap of a 400 m track gives 400 m of distance and zero displacement. Average speed divides total distance by total time rather than averaging instantaneous values, which is why a 6 m/s climb and a 10 m/s descent over the same stretch average to 7.5 m/s.
distance-time 图：斜率就是速度
distance-time 图的纵轴是距离，横轴是时间，一段直线的斜率就是这一段的速度。水平线表示物体静止，斜率越大走得越快，向上弯的曲线表示正在加速。考纲 2.1(b) 要求读懂 speed-time 与 distance-time 两种图，2.1(d) 专门要求用 velocity-time 图求加速度和路程，两份要求别混。常见的错误是把 distance-time 图下面的面积当成路程，那个面积没有任何物理意义。另一种错误是在曲线上随手量一段弦当斜率，正确做法是画切线，切线斜率才是那一瞬间的速度。答读图题时先把两轴的单位写在草稿上，单位看错整题白算。
On a distance-time graph the vertical axis is distance and the horizontal axis is time, so the gradient of a straight section is the speed for that section. A horizontal line means the object is stationary, a steeper line means faster motion, and an upward curve means the speed is rising. The area under such a graph means nothing at all, which is the trap that catches candidates who have memorised area formulas without attaching them to a graph type. Where the line curves, the gradient has to come from a tangent drawn at the point of interest, not from a chord joining two distant points.
velocity-time 图：斜率与面积各管一件事
velocity-time 图的读法正好反过来：斜率是加速度，图线下面的面积是路程。2.1(d) 把这句话写成考点，要求用 velocity-time 图求 acceleration 和 distance travelled。面积要按图形拆开算，矩形加三角形，或者直接数格子，考纲的数学要求里明确写了 counting squares 这一手。负斜率表示减速，图线落到时间轴以下表示反方向运动，那部分面积要取负值再加进去。很多学生以为面积一定是正的，来回运动的题就错在这里。作图时把每一段的起止时间标出来，面积分成几块一目了然。
A velocity-time graph reverses the reading: the gradient gives acceleration and the area beneath the line gives the distance travelled. The specification asks candidates to use such graphs for exactly those two purposes, and its mathematics section adds counting squares as an accepted method for irregular shapes. A negative gradient means deceleration, and a line dipping below the time axis means motion in the opposite direction, so that area has to be subtracted rather than added. Splitting the area into rectangles and triangles before doing any arithmetic keeps the marks safe.
km/h 与 m/s：先除 3.6 再动笔
km/h 换 m/s 只除 3.6，72 km/h 就是 20 m/s，30 mph 约 13.4 m/s。这一步错了，后面 F = ma 与停止距离会全部连锁错。考纲的数学要求写着能做估算、能在没有计算器时估出结果，所以 100 km/h 记成 28 m/s 足够用，不必写 27.78。答卷上单位要跟数字一起写，m/s 与 km/h 混着填是阅卷时最常见的扣分点之一。有效数字按题目给的数据定，题目给两位有效数字，答案就写两位。考试不带计算器也能做，前提是先把换算这一步练成条件反射。
Converting km/h to m/s means dividing by 3.6, so 72 km/h becomes 20 m/s and 30 mph is roughly 13.4 m/s. Get this step wrong and the error travels straight into F = ma and into every stopping distance calculation. The specification expects estimates without a calculator, so 28 m/s for 100 km/h is good enough, and units belong on the answer line with the same number of significant figures as the data given. Kinetic energy questions punish the same slip twice, because the speed is squared there.
加速度公式与负号怎么处理
加速度写成 a = (v - u) / t，v 是末速度，u 是初速度，t 是这一段用的时间。一辆车 9.5 s 内从静止到 100 km/h，先把 100 km/h 换成 28 m/s，再算 28 除以 9.5，得 2.9 m/s²。刹车时末速度小于初速度，答案自然是负数，写 deceleration 就要取正数并说明方向。考纲 2.1(c) 把 speed = distance / time 与这条加速度式并列在同一行，两个公式都可能要先移项再代入。Foundation 层级的考生不需要自己变换公式的主项，试卷开头会给出公式表。代入之前先写清哪个是 u、哪个是 v，符号错位是这一步最常见的失分。
Acceleration is a = (v - u) / t, with v the final velocity, u the initial velocity and t the time taken. A car reaching 100 km/h from rest in 9.5 s first converts to 28 m/s, then divides by 9.5 to give about 2.9 m/s². A braking case simply produces a negative answer, which is reported as a positive deceleration with the direction stated. Foundation tier candidates are not expected to change the subject of an equation, and every paper prints the equation sheet at the front, so the skill being tested is choosing the right equation rather than rearranging it.
自由落体、g 与终端速度
地球表面 1 kg 的物体重约 10 N，考纲把 g 的这个近似值直接写进 2.2(e)，所以用 W = m g 时取 10 N/kg 就够。空气阻力随速度增大，落体受到的合力越来越小，加速度跟着变小，最后合力为零，速度不再增加，这就是 terminal speed。2.2 指定的实验就是测下落物体的终端速度，器材不复杂，纸锥或小球加刻度尺和计时器即可。很多学生以为重的物体一定落得更快，真空里两者同时落地，空气里差别来自阻力与形状，不来自质量本身。同一颗石子从 2 m 高的桌面落下，忽略阻力时落地速度约 6.3 m/s，这个数用 g = 10 估也够。
On the Earth's surface a 1 kg mass weighs about 10 N, and the specification writes that approximation into 2.2(e), so W = m g with g = 10 N/kg is the expected route. Air resistance grows with speed, the resultant force falls, acceleration falls with it, and once the two forces balance the speed stops rising at terminal speed. The required practical for 2.2 measures terminal speed for a falling object, using little more than a paper cone or a small ball, a ruler and a timer. In a vacuum the mass of a falling body changes nothing about how fast it falls.
牛顿第一定律与惯性
牛顿第一定律说，物体在不受合力时会保持静止或匀速直线运动，惯性就是这种不肯改变的性质，质量是惯性的量度。2.2(a) 与 2.2(b) 把这两条分开列，答概念题时要能原句写出来。汽车急刹时人继续向前，不是有一股力把人推出去，而是人保持原来的运动状态，安全带提供的是减速所需的合力。很多学生以为惯性是一种力，写成惯性力就丢分。质量大的物体惯性大，同样的力改变它的运动更难。答题时把「没有合力」这个前提写出来，比只背结论更容易拿到过程分。
Newton's first law says a body with no resultant force stays at rest or keeps moving in a straight line at constant speed, and inertia is the name for that reluctance to change, with mass as its measure. In a braking car the passenger keeps moving forward not because a force pushes them but because nothing has yet acted to slow them, and the seat belt supplies the resultant force that does. Inertia is not a force, which is the single most common conceptual error in this topic, and the phrase to keep in an answer is the absence of a resultant force.
牛顿第二定律 F = m a
第二定律的考纲写法就是 resultant force = mass × acceleration，即 F = m a。2.2(c) 先讲比例关系：合力越大加速度越大，质量越大加速度越小，2.2(d) 才给出公式本身。用的时候先算合力再代质量，常见的错误是把某一个力直接当成合力，漏掉重力或摩擦力。举例：2 kg 的物体受 12 N 向前的力和 4 N 的阻力，合力 8 N，加速度 4 m/s²。同一道题要 weight 时用 W = m g，取 g = 10 N/kg 得 20 N，两个数不能混用。单位也要跟着走，N 除以 kg 才是 m/s²。
The second law appears in the specification as resultant force = mass × acceleration, written F = m a. Clause 2.2(c) sets out the proportionalities first, a larger resultant force giving a larger acceleration and a larger mass giving a smaller one, and 2.2(d) then states the equation. Work out the resultant force before dividing by mass: a 2 kg body pulled forward by 12 N against 4 N of friction has 8 N resultant and accelerates at 4 m/s², while its weight of 20 N is a separate quantity that must not be mixed into the same line. Newtons divided by kilograms give m/s², and the unit check catches most slips.
牛顿第三定律与平衡力的区别
第三定律说两个物体之间的作用力与反作用力大小相等、方向相反、作用在同一条直线上，关键在「两个物体」这四个字。人推墙，墙也推人；船桨推水，水推船前进。常见的错误是把它和平衡力搞混：平衡力作用在同一个物体上，作用力与反作用力分别作用在两个物体上，永远不能相互抵消。考纲 2.2(g) 只要求能陈述这条定律，简答题里却常常要求举一个例子并指出两个受力物体。写例子时把两个物体都点明，分数就稳。答题纸上画两个小方块和箭头，比写一段文字更省时间。
The third law states that the forces two bodies exert on each other are equal in size, opposite in direction and along the same line, and the phrase that matters is two bodies. A hand pushes a wall and the wall pushes the hand back; an oar pushes water backwards and the water pushes the boat forwards. Balanced forces act on one body and cancel, whereas an action-reaction pair acts on two different bodies and never cancels, which is the distinction examiners look for. Naming both objects in the example is usually worth the mark on its own.
停止距离：反应距离加制动距离
停止距离由反应距离和制动距离相加得到，考纲 2.1(e) 要求掌握 reaction time、thinking distance、braking distance 与 overall stopping distance 四个词。gov.uk 的 Highway Code 给出典型值：30 mph 合计 23 m，其中反应 9 m、制动 14 m；50 mph 合计 53 m，其中反应 15 m、制动 38 m。速度翻倍时制动距离约变成四倍，因为动能按速度的平方增长，60 mph 的制动距离 55 m 已经接近 30 mph 的四倍。反应距离只随速度线性增长，两者的差别正好解释了为什么超速的后果比直觉严重。影响这些距离的因素包括疲劳、酒精、分心、湿滑路面、轮胎与刹车状态，2.1(f) 还要求用这些数据讨论限速与安全带。
Stopping distance is thinking distance plus braking distance, and 2.1(e) expects all four terms: reaction time, thinking distance, braking distance and overall stopping distance. The Highway Code on gov.uk gives typical figures of 23 m at 30 mph, split into 9 m of thinking and 14 m of braking, and 53 m at 50 mph, split into 15 m and 38 m. Braking distance rises roughly with the square of the speed because kinetic energy does, so doubling speed nearly quadruples it, while thinking distance only doubles. That asymmetry is the physics behind speed limits, and 2.1(f) asks candidates to use the data to argue about them.
分层卷的差别与 2.4 的后续
两个层级的差别不只在难度：Higher 只发 A* 到 D，Foundation 只发 C 到 G，选错层等于把上限提前锁死。试卷开头给出公式表，Foundation 考生不必自己变换公式主项，Higher 考生要能熟练移项。2.1 之后还有 2.4 Further Motion Concepts，那里才把匀加速直线运动的一组公式和动量守恒拿出来，先把 2.1 的图像与加速度练熟再进 2.4。2.3 的动能与重力势能会绕回运动学，把 v 与 h 接上，题目常常跨小节组合。复习顺序按 2.1 到 2.4 走，图像是贯穿全部小节的主线，每道题先在草稿上画一条线再动笔。
The tiers are not only about difficulty, since Higher awards A* to D and Foundation awards C to G, so the choice fixes the ceiling before the exam. Every paper prints the equation sheet, Foundation candidates are not required to rearrange formulas, and Higher candidates are expected to do so fluently. Topic 2.4, Further Motion Concepts, then adds the equations for uniformly accelerated motion in a straight line together with momentum, so the graph and acceleration work from 2.1 should be secure before that point. Kinetic and gravitational potential energy in 2.3 loop back into the same graphs, which is why exam questions often combine sections.
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