WJEC物理 GCSE 运动 速度 加速度 图像
运动是 WJEC GCSE Physics Unit 2 的开篇内容，也是整张卷子里最容易拿分、同时最容易因为单位与图像丢分的一块。它把速度、加速度、图像、力与动量串成一条线，公式本身不多，但每个公式都有使用条件。这篇文章按考试的出题顺序把它拆成十三块，每一块给出定义、常见数值与失分动作，方便对着卷子逐条核对。
Motion opens Unit 2 of WJEC GCSE Physics and it is one of the most reliable sources of marks, provided the units and the graphs are handled carefully. The ideas run from speed and acceleration through motion graphs to force, weight and momentum, and every equation carries conditions attached to it. This article breaks the topic into thirteen blocks with definitions, worked numbers and the mistakes that cost marks.
Unit 2 的分值与试卷结构
WJEC GCSE Physics 的课程代码是 3420，运动内容放在 Unit 2 Forces, Space and Radioactivity 里，与力、功与能、动量、恒星和放射性共用一张卷子。这张卷子一小时四十五分钟，满分八十分，占整科的百分之四十五；Unit 1 Electricity, Energy and Waves 也用同样的分值，校内的实践考核占剩下的百分之十。Unit 2 分 Foundation 与 Higher 两层，Foundation 的成绩上限是 C，Higher 覆盖 A* 到 D，终端速度、动量与三个运动方程只在 Higher 的要求里出现。WJEC 官网公布的 spec 写明数学技能至少占整科百分之三十，所以运动这一块的图像斜率、面积与单位换算不是附加内容。卷首会印一张公式表，速度、加速度、合力、动量这些公式不必背，但要会挑。阅卷时按步给分，公式与代入写对、后面算错，方法分仍然拿得到。错得最多的是把式子列对却漏了单位换算，八十分里往往会丢两三分。
Motion sits inside Unit 2 Forces, Space and Radioactivity, coded 3420, sharing one paper with forces, energy, momentum, stars and radioactivity; that paper runs 1 hour 45 minutes and carries 80 marks, or 45% of the whole qualification. Unit 1 covers electricity, energy and waves at the same weight while the school-based practical assessment takes the final 10%, and WJEC's published specification requires mathematical skills to make up at least 30% of the subject. Foundation tier is capped at grade C against Higher tier's A* to D, so terminal velocity, momentum and the equations of motion only appear on the Higher list; equations for speed, acceleration, resultant force and momentum are printed with the paper.
速率与速度的方向差别
速度的定义是单位时间内走过的路程，公式写成 v = s / t，用 400 米跑道在 80 秒内跑完来算，平均速度为 5.0 m/s。速度则多一个方向，说 5.0 m/s 向东才算速度，只说 5.0 m/s 是速率。很多学生以为方向只是文字修饰，实际上一旦方向改变速度就改变，绕圈跑一整圈的平均速度为零，而平均速率不是零。常见单位换算是 1 m/s 等于 3.6 km/h，所以 20 m/s 就是 72 km/h，反过来 90 km/h 约等于 25 m/s。平均速度用总路程除以总时间，中途停顿的时间照样要算进去，这一点在公交车或列车题目里最常考。这一题型的失分通常不是算错，而是把分段速度相加再除以段数，当成整体平均速度使用。阅卷时只要过程里出现总路程与总时间两行，即使答案的小数位与标准答案略有差别也能给分。
Speed measures how much distance is covered each second using v = s / t, so a 400 m lap run in 80 s gives an average speed of 5.0 m/s; velocity carries exactly the same number plus a direction. A full lap therefore has zero average velocity but a non-zero average speed, and unit conversion runs through most questions, with 1 m/s equal to 3.6 km/h, 20 m/s the same as 72 km/h and 90 km/h about 25 m/s. Averaging speeds by adding the two numbers and halving them is the classic trap on bus and train questions, because total time must include every stationary period.
距离-时间图的斜率读数
距离-时间图的纵轴是距离，横轴是时间，直线段的斜率就是这一段的速度，水平线代表静止。最陡的那一段速度最大，很多学生以为曲线最高点速度最大，其实要看坡度而不是高度。把两点数据代入斜率就能算出数值，例如 20 秒内走了 100 米，斜率就是 5.0 m/s。曲线表示变速运动，这时只能算平均速度，某个瞬间的速度要用该点的切线来估计。题目常问某一段是否匀速，判断标准是这条线是不是直线，弯了就说明速度在变。上坡型与下坡型在同一张图上代表方向相反，回到起点时距离会重新变小，这一点容易与静止混起来。常见的错误是坐标轴看反，时间与距离弄混之后所有斜率都算反。
On a distance-time graph the gradient of a straight line is the speed for that section and a flat line means the object is stationary; the steepest section always gives the highest speed. The highest point on a curved graph is not the fastest point, because speed follows the slope rather than the height, so a 100 m section covered in 20 s reads 5.0 m/s, and a curve means only an average can be quoted. The tangent at one point gives an instantaneous value, a downward line returning towards the start does not mean rest, and mixing up the two axes reverses every gradient.
速度-时间图的斜率与面积
速度-时间图的斜率是加速度，图线与时间轴之间的面积是位移，这两条规则在 Unit 2 里几乎每张卷子都会用到。以从零加速到 12 m/s 用 3.0 秒为例，斜率 12 / 3.0 = 4.0 m/s^2，三角形面积 0.5 x 3.0 x 12 = 18 米。若之后保持 6.0 m/s 走 5.0 秒，这一段面积是 30 米，两段相加就是全程位移 46 米。面积规则只对匀速与匀加速的直线段成立，曲线段要用数格子或估算来求，误差写清楚仍然给分。学生最常把速度-时间图与距离-时间图的面积含义互换，把图线下的面积当成速度再算一遍。WJEC 官方阅卷报告里提到的另一类失分是用最高速度乘总时间代替面积，这会把加速阶段的位移算大一截。
The gradient of a velocity-time graph gives acceleration and the area between the line and the time axis gives displacement, and both rules appear on almost every Unit 2 paper. Accelerating from rest to 12 m/s in 3.0 s gives a gradient of 4.0 m/s^2 and a triangular area of 18 m, while a further 5.0 s at 6.0 m/s adds 30 m for a total displacement of 46 m. Areas work only for constant speed or uniform acceleration, and WJEC's examiner report notes that candidates often multiply the top speed by the whole time instead of using the area, which overstates the distance gained while accelerating.
加速度公式与减速的负号
加速度的定义是单位时间内速度的变化量，用 a = Δv / t 计算，Δv 等于末速度减初速度。24 m/s 在 8.0 秒内减到零，代入得 -3.0 m/s^2，这个负号表示减速，写成减速 3.0 m/s^2 也可以。单位是 m/s^2，意思是每秒钟速度改变多少米每秒，不要写成 m/s。正负号取决于方向约定，先规定向右为正，向左加速就会出现负值，答案里的符号与文字说明要一致。很多学生以为只有速度变小才算加速度变化，其实匀速转弯也在加速，因为方向变了。计算题一般给两三个数据，先判断已知量是初速度、末速度还是变化量，再选公式，比直接套式快。这一步最容易出错的地方是把时间单位写成分钟，卷面给的是 min，公式里要换成秒。
Acceleration is the rate of change of velocity, calculated as a = Δv / t where Δv is final velocity minus initial velocity; slowing from 24 m/s to rest in 8.0 s gives -3.0 m/s^2. The unit m/s^2 means metres per second of velocity gained every second, and the sign depends on the direction chosen as positive, so the stated convention has to match the working. Turning at constant speed still counts as acceleration because direction changes, and any time given in minutes must be converted to seconds before it enters the equation.
停车距离里反应与制动的分工
停车距离由两部分组成，反应距离是驾驶员从看到情况到踩下刹车之间走过的路程，制动距离是刹车起作用后滑行的路程。反应距离随速度线性增大，制动距离大约随速度的平方增大，所以速度翻倍，制动距离接近四倍。英国交通部 Highway Code 的典型数字是 30 mph 约 23 米、60 mph 约 73 米，可以用来比较趋势，不要当作精确计算答案。影响反应时间的因素有酒精、疲劳、药物与分心，影响制动距离的有路面湿滑、轮胎磨损与刹车状况。常见的错误是只答速度一个因素，题目问两个以上原因时要分开写，反应与制动各给一分。题目还常问下雨天为什么车距要加大，落点应是制动距离变大，而不是反应距离变长。阅卷时看到学生把停车距离写成单一数字而不分两段，通常只能拿到一半分。
Stopping distance splits into thinking distance, covered while the driver reacts, and braking distance, covered once the brakes bite; thinking distance rises in proportion to speed while braking distance rises roughly with the square of speed. The UK Department for Transport Highway Code quotes about 23 m from 30 mph and about 73 m from 60 mph, which is useful for comparing trends rather than for exact answers. Alcohol, tiredness, medication and distraction lengthen reaction time, whereas wet roads, worn tyres and poor brakes lengthen braking distance, so a question asking for two factors expects one from each group.
牛顿第一定律与惯性的判据
牛顿第一定律说的是，物体在合力为零时保持静止或匀速直线运动，这条结论也叫惯性定律。惯性是物体保持原有运动状态的性质，只与质量有关，质量越大惯性越大，与速度无关。很多学生以为速度越大惯性越大，这是选择题里出现频率最高的干扰项。生活中系安全带的理由就是惯性：车突然停下时人还在向前运动，安全带提供减速的力。放在桌上的书受到重力与支持力，两力大小相等方向相反，合力为零，所以书保持静止。解题时先判断合力是否为零，再判断运动状态，顺序颠倒容易把受力分析写乱。这一步最容易在多个受力里漏掉一个力，最后把合力算成非零值。
Newton's first law states that an object stays at rest or moves at constant velocity when the resultant force on it is zero, which is why the law is also called the law of inertia. Inertia depends only on mass and never on speed, so heavier objects resist changes to their motion more strongly, and the most common distractor in multiple-choice questions links inertia to velocity. A book resting on a table has equal and opposite weight and support forces giving zero resultant force, and seat belts exist because passengers keep moving forward when a car stops suddenly.
合力与 F = ma 的代入
合力是所有作用力相加的结果，把向右的力减去向左的力就得到合力，单位是 N。F = ma 里的 F 必须是合力，不是某一个力，1200 kg 的车受 3000 N 合力时加速度为 2.5 m/s^2。受力图里箭头长度要反映大小，方向相反的两个力要分别标注，漏画一个力是画图题常见的失分。摩擦力的方向始终与相对运动或运动趋势相反，牵引力与摩擦力相等时物体匀速运动，加速度为零。题目给质量与加速度问力，或者给力与质量问加速度，两种问法都要先写公式再代入数值。阅卷时公式写对、代入正确、单位齐全，即使最后一步除错也有方法分。学生最常把合力写成某一个单独的力，比如把推力直接当合力代进 F = ma。
The resultant force is the sum of all the forces acting, found by subtracting opposing forces, and the F in F = ma is always that resultant rather than one single force. A 1200 kg car with a resultant force of 3000 N accelerates at 2.5 m/s^2, and force diagrams must show arrow lengths in proportion while labelling every acting force. Friction always opposes relative motion, so an object moves at constant velocity once the driving force matches it, and marks are awarded for the equation and the substitution even when the final division goes wrong.
重量、质量与自由落体
质量是物体所含物质的多少，单位是 kg，重量是重力对物体施加的力，单位是 N，两者不能互换。公式 W = mg 里的 g 是重力场强度，地球上取 9.8 N/kg，60 kg 的人重量约 588 N。月球上的 g 约为 1.6 N/kg，同一个人在月球上重量只有 96 N，但质量仍然是 60 kg，这一问几乎每年都会出现。忽略空气阻力时，所有物体在同一重力场里的加速度相同，与质量无关，纸片与铁球只在有空气时落得不一样。自由落体 2.0 秒的末速度是 9.8 x 2.0 = 19.6 m/s，下落距离用 0.5 x 9.8 x 2.0^2 = 19.6 m。很多学生以为重的物体落得快，这个直觉在真空中不成立。这一步最容易把 N/kg 与 m/s^2 当成两种不同的量，其实它们数值相等。
Mass measures the amount of matter in kilograms while weight is the gravitational force in newtons, and the two are linked by W = mg with g taken as 9.8 N/kg on Earth, giving a 60 kg student a weight of about 588 N. On the Moon g falls to roughly 1.6 N/kg, so the same student weighs about 96 N but still has a mass of 60 kg, a question asked almost every year. In a vacuum all objects fall with the same acceleration whatever their mass, whereas a falling ball reaches 19.6 m/s after 2.0 s and covers 19.6 m.
终端速度的四段过程
物体从静止下落时先受到重力与阻力，阻力较小，合力向下，加速度最大。速度增大之后阻力增大，合力变小，加速度随之减小，速度还在增加但增加得越来越慢。当阻力增大到与重力相等时，合力为零，加速度为零，速度不再变化，这个恒定速度就是终端速度。换成在液体中下落，过程一样，但阻力更大，终端速度更低，实验里常用小球与黏稠液体来演示。空气阻力随速度增大而增大，所以伞张开之后终端速度下降，人落地更安全。题目常问速度-时间图上哪一段对应终端速度，答案是图线变平的那一段。常见的错误是把终端速度说成最大速度或匀加速的终点，漏掉加速度为零这个条件。
A falling object begins with a large downward resultant force because drag is small, which gives it its greatest acceleration. As speed rises, drag rises with it and the resultant force shrinks, so acceleration falls while velocity keeps increasing more slowly; once drag equals weight the resultant force and acceleration are both zero and the speed stays constant at terminal velocity. The same sequence happens in a liquid at a lower terminal velocity, and on a velocity-time graph the flat section marks that steady speed.
三个运动方程的选用条件
匀加速直线运动可以用三个运动方程，v = u + at 不含位移，x = (u + v) t / 2 不含加速度，v^2 = u^2 + 2ax 不含时间。选式的规则是看题目没有给哪个量，让那个量从方程里缺席，比先算出中间量再往下走省时间。以 20 m/s 的车以 4.0 m/s^2 减速到停下为例，用 v = u + at 得 t = 5.0 秒，用 v^2 = u^2 + 2ax 得 x = 50 米，两条路的结果一致。方程只适用于加速度恒定的直线运动，图线是曲线或者方向改变时不能直接套用。很多学生以为三个方程要一起用，其实一道题通常一个方程就够，多用反而多一处算术风险。题目要求 show that 时，过程要写到每一步代数变形，只写结果不给分。这一步最容易把初速度当成零，把匀减速题写成自由落体。
The three equations of motion for uniform acceleration are v = u + at, x = (u + v) t / 2 and v^2 = u^2 + 2ax, and choosing between them comes down to which quantity the question never mentions. A car travelling at 20 m/s and decelerating at 4.0 m/s^2 stops in 5.0 s by the first equation and covers 50 m by the third, so the two routes agree. They apply only to straight-line motion with constant acceleration, and show that questions need the algebra written out rather than a final number.
动量守恒与 Δp 除以 t
动量等于质量乘速度，写成 p = mv，单位是 kg m/s，方向与速度一致。封闭系统内碰撞前后的总动量守恒，两个物体相撞时一方动量减小，另一方增加同样的数值。1200 kg 的车以 8.0 m/s 行驶，动量为 9600 kg m/s，撞上静止物体之后动量在两者之间重新分配，总量不变。力与动量的关系写成 F = Δp / t，意思是动量变化越快需要的力越大，安全气囊与缓冲带都是靠延长作用时间把力降下来。0.5 kg 的球以 4.0 m/s 运动，动量是 2.0 kg m/s，接住它比把它弹回所需的力小，因为反弹的动量变化更大。常见的错误是把动量与动能混用，动量是矢量而动能是标量，单位也不一样。阅卷时守恒式必须写出碰撞前与碰撞后的总动量两行，只写一个答案会扣分。
Momentum is mass multiplied by velocity, p = mv, measured in kg m/s and directed along the velocity, and in a closed system the total momentum before and after a collision stays the same. A 1200 kg car at 8.0 m/s carries 9600 kg m/s, and catching a 0.5 kg ball at 4.0 m/s takes less force than bouncing it back because the change in momentum is larger. The relation F = Δp / t explains why airbags and crash barriers lengthen the contact time to reduce the force, and the working must show the totals before and after the collision.
阅卷失分点与三周复习安排
WJEC 官网公布的 GCSE Physics Examiners Report Summer 2024 指出，定量题整体好于定性题，最常见的失分是替换数字时没有换算单位、进位方式不对、只写答案不写过程。同一份报告还写明，涉及斜率、正比与比值计算的问题只有很强的考生答得出，说明这类题要多练数据解读而不是死记公式。复习头一周可以把速度、加速度与两类图像的斜率面积做成一张对照表，每个公式配一道真题。第二周专攻受力分析与牛顿定律，把合力、重量与终端速度串起来做三到四道综合题。第三周按考试时间做两套限时卷，选择题部分控制在 25 分钟内完成。每套卷子订正时记录失分类型而不是抄答案，单位与进位错误单独立一栏。这样练三周，八十分里最容易丢的那五六分通常能先稳住。
WJEC's published Physics Examiners Report for Summer 2024 records that candidates handled quantitative questions better than qualitative ones, with the recurring losses coming from unconverted units, poor rounding and answers written without working. The same report states that only the very able answered questions based on gradients, proportionality and ratios, which points to more practice on data interpretation. A three-week plan works well: one week on speed, acceleration and graph slopes with a past-paper question attached to each equation, one week on force diagrams and Newton's laws, then two timed papers in the final week with an error log sorted by loss type.
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