Edexcel物理 GCSE 运动 速度 加速度 动量
运动这一章是 Edexcel GCSE 物理的 Topic 1 Motion and forces，也是后面所有计算题的语言基础。它看起来只是套公式算速度，真正拉开差距的地方在读数、看图和单位换算。1PH0 两张卷各 1 小时 45 分钟、100 分、各占 50%，Paper 1 考 Topic 1 到 7，运动与力全部落在这一张卷里。Paper 2 考 Topic 8 到 15，题目仍会回头用运动的思路，比如能量与波里面的速算。很多学生以为这一章背六个公式就能过关，结果在图像面积题上连续丢分。下面按考点顺序把公式、图像读法与阅卷口径拆开讲。
Motion and forces is the opening topic of the Edexcel GCSE Physics course, and it supplies the calculation language that every later topic reuses; scalars, vectors, units and graphs come back in energy, waves and astronomy questions. Both papers are 1 hour 45 minutes long and worth 100 marks each, with Paper 1 covering Topics 1 to 7 and Paper 2 covering Topics 8 to 15 while still leaning on motion reasoning. Many students treat the chapter as six formulas to memorise, then drop marks on the areas under velocity-time graphs.
一、Topic 1 在卷面上的位置 / Where Topic 1 Sits in the Papers
Topic 1 的题在 Paper 1 里通常以两三道小题的形式出现，分值从 1 分到 6 分都有。官方 spec 把这一章拆成标量与矢量、速度与加速度、牛顿三定律、动量与刹车距离几块，每块都能单独出题。计算题的给分通常分三步：写出公式、代入带单位的数值、给出符合有效数字要求的答案。1PH0 从 2016 年 9 月起施教，2018 年首次考试，Foundation 卷目标 1 到 5 级，Higher 卷覆盖 4 到 9 级。阅卷时最常见的情况是学生直接写答案，公式分与代入分一起丢掉。公式分在 Edexcel 的评分方案里通常只有 1 分，但一道 6 分题里足够让等级滑一档。
Topic 1 questions usually arrive as two or three separate items worth anything from one mark to six; the mark scheme rewards the formula, the substitution with units, and the final answer at the required number of significant figures. Specification 1PH0 came into teaching in September 2016 with first assessment in 2018, and the Foundation tier targets grades 1 to 5 while the Higher tier covers 4 to 9. Writing the answer alone, however accurate, throws away the first mark of every calculation.
二、标量、矢量与单位换算 / Scalars, Vectors and Units
标量只有大小，矢量既有大小又有方向，距离、速率与质量属于前者，位移、速度、力与加速度属于后者。单位换算每年都考，1 km 等于 1000 m，1 m/s 等于 3.6 km/h，于是 20 m/s 换成 72 km/h。换算方向写反是常见的错误，把 20 m/s 写成 5.6 km/h 就是这样来的。答案必须带单位，m/s 与 m/s^2 是两个不同的单位，加速度写成 m/s 直接不给分。有效数字按题目要求处理，题目没有要求时通常保留两位或三位，中间步骤多留一位避免累积误差。3.6 这个系数来自一小时 3600 秒除以一公里 1000 米，记住来源比死记数字稳。
Scalars carry magnitude only while vectors carry magnitude and direction, which is why distance and speed sit in a different group from displacement and velocity; forces and accelerations are vectors too. The conversion that trips people up is speed, since 1 m/s equals 3.6 km/h, so 20 m/s is 72 km/h rather than 5.6 km/h. Units belong on every answer, and an acceleration written as m/s instead of m/s squared scores nothing.
三、平均速度与瞬时速度 / Average and Instantaneous Speed
平均速度是总路程除以总时间，瞬时速度要看很短一段路程对应的很短一段时间。日常说的速率指大小，速度还带方向，向右 5 m/s 与向左 5 m/s 速率相同、速度不同。常见的一类题是往返行程：去程 30 km 用 30 分钟，回程 30 km 用 45 分钟。这时平均速度要用 60 km 除以 1.25 小时得到 48 km/h，不是把两个速率平均成 50 km/h。另一类题给速度时间图问某一刻的瞬时速度，读出纵坐标即可。很多学生以为平均速度就是几个速度相加除以个数，这类题因此稳丢 2 分。
Average speed is total distance divided by total time, whereas instantaneous speed needs a very short distance paired with a very short time interval; speed is the magnitude and velocity adds direction, so 5 m/s to the right and 5 m/s to the left share a speed but not a velocity. A classic item is a return journey with 30 km covered in 30 minutes and another 30 km taking 45 minutes, where the answer is 48 km/h rather than the 50 km/h you get by averaging the two speeds. Light gates or frame-by-frame video timing give the instantaneous value, and the shorter the measured distance, the closer the reading comes.
四、距离时间图的斜率 / Gradients on Distance-Time Graphs
距离时间图的纵轴是距离、横轴是时间，直线上任一点的斜率就是速率。水平线段表示静止，斜向下的线段表示物体正在返回起点。曲线段斜率随时间变大表示加速，变小表示减速，判断标准只看曲线陡不陡。作图题的要求是点画准、线连直、坐标轴标注带单位，评分方案对轴标签单独给分。算斜率要在图上取两个相距较远的点，这样读数误差小得多。取相邻两点容易把 0.5 格的误差放大成 0.3 m/s 的偏差，图上两个点的距离要肉眼可见地拉开。
On a distance-time graph the gradient of the line is the speed, a flat section means the object is stationary and a downward slope means it is heading back towards the start; curvature shows acceleration or deceleration. Gradients should be taken between two points as far apart as possible, because reading adjacent points turns a small plotting error into a large speed error. Graph questions are marked on axis labels with units, plotted points and straight joining lines, so a correct number with an unlabelled axis still loses marks.
五、速度时间图的斜率与面积 / Slope and Area on Velocity-Time Graphs
速度时间图的斜率是加速度，曲线下的面积是位移，这两句话能覆盖这一章大半的图像题。水平线段表示匀速运动，此时加速度为零，斜向上的直线表示匀加速。面积题分两类：矩形加三角形可以拆开算，梯形用上底加下底乘高除以 2。负速度与减速要分清，速度为负表示朝反方向运动，减速是速度大小在变小。求位移时时间轴下方的面积算负值，问路程则全部取正值。学生最常把面积当成距离，还忘记看坐标轴刻度，纵轴每格 2 m/s、横轴每格 1 s 时一格代表 2 m。
The gradient of a velocity-time graph is acceleration and the area beneath it is displacement, a pair of rules that answers most graph questions in this topic; a flat line means steady velocity with zero acceleration. Areas split into rectangles and triangles, or into a trapezium using half the sum of the parallel sides multiplied by the height, and negative velocity means motion in the opposite direction rather than deceleration. Reading the scale matters, since a grid square of 2 m/s by 1 s stands for 2 m of displacement, not 1 m.
六、匀加速公式的选用 / Choosing the Uniform Acceleration Equations
匀加速常用的三个式子是 v = u + at、s = ut + 0.5at^2、v^2 = u^2 + 2as。选式子的方法看题目给了什么、问什么：知道初速度、时间与加速度求末速度用第一式。求位移用第二式，不涉及时间时用第三式。刹车计算题几乎都用第三式，因为反应时间之后那段减速过程只给速度、加速度和距离。单位要统一成米和秒，把 72 km/h 直接代入第三式是常见的错误，正确做法是先换算成 20 m/s。算出的负加速度不要慌，符号表示方向与初速度相反，答题时说明减速即可。
For constant acceleration the working equations are v equals u plus at, s equals ut plus half at squared, and v squared equals u squared plus 2as; the choice depends on which quantity is missing. Braking questions almost always use the third form, because after the reaction time you know the initial speed, the deceleration and the distance. Speeds must be converted to metres per second first, and a negative acceleration simply means the direction opposes the initial motion.
七、牛顿第一定律与惯性质量 / Newton's First Law and Inertial Mass
牛顿第一定律说物体不受合力时保持静止或匀速直线运动，这里的合力是关键。受力平衡不等于没有受力，重力和支持力互相抵消时物体照样受力。惯性质量衡量改变运动状态的难易程度，质量越大越难加速，质量与重量是两回事。典型场景是匀速行驶的车、匀速下降的跳伞者和水平滑行的冰壶，三者合力都为零。判断时要先看运动状态有没有变化，速度大小与方向都不变才算匀速直线运动。很多学生以为匀速就是不受力，选择题因此选错，圆周运动的速度方向一直变、合力不为零。
Newton's first law keeps an object at rest or moving in a straight line at constant speed when the resultant force is zero, and the resultant force is what the law is really about; balanced forces are not the same as no forces. Inertial mass measures how hard it is to change an object's motion, and it is a different quantity from weight. The usual scenarios are a car cruising at a steady speed, a skydiver falling at terminal velocity and a curling stone sliding across level ice, and in each case the forces cancel.
八、F = ma 与小车核心实验 / F = ma and the Trolley Core Practical
牛顿第二定律写成 F = ma，力用牛顿、质量用千克、加速度用 m/s^2，三者单位必须对应。Edexcel 的核心实验用小车、配重片和光门或数据记录仪，通过改拉力或改质量来测加速度。关键控制变量是质量与拉力每次只改一个，同时改两个会让数据无法解释。常见错误是忘记小车本身的质量，把配重算成总质量，得到的加速度会明显偏大。数据记录仪给出速度与时间的直线，取斜率就是加速度，比手工打点计时器抄点省事。处理数据时先看直线是否过原点，不过原点说明摩擦力没有抵消。
Newton's second law is written as force equals mass times acceleration, with newtons, kilograms and metres per second squared as the matching units; the core practical uses a trolley with added masses plus light gates or a data logger. Only one variable should change at a time, because altering the mass and the force together leaves the results impossible to interpret. A frequent mistake is forgetting the mass of the trolley itself, which makes the calculated acceleration too large, so check that the plotted line passes through the origin.
九、重量、质量与自由落体 / Weight, Mass and Free Fall
重量是重力作用在质量上的力，写成 W = mg，在 GCSE 里 g 通常取 9.8 N/kg。质量 60 kg 的学生的重量是 588 N，这个数字几乎每年都在题里出现。质量在任何地方都不变，重量会随 g 改变，同样的 60 kg 在月球上只有约 98 N。忽略空气阻力时所有物体自由下落的加速度相同，都是 9.8 m/s^2，与质量无关。因此羽毛和铁球在真空管里同时落地，这是解释题的经典情境。很多学生以为重的物体落得快，用重力加速度与质量无关这一句就能把两分的说明题写满。
Weight is the force of gravity acting on a mass, given by W equals mg with g taken as 9.8 N/kg at GCSE, so a 60 kg student weighs 588 N; mass stays the same everywhere while weight changes with g. In free fall without air resistance every object accelerates at 9.8 m/s squared regardless of its mass, which is why a feather and a steel ball land together in a vacuum tube. That single fact carries the explanation mark, so quote it rather than restating the experiment.
十、终端速度与空气阻力 / Terminal Velocity and Air Resistance
物体下落时空气阻力随速度增大，当阻力增大到与重力相等，合力为零，速度不再变化。这个不再变化的速度就是终端速度，跳伞员先加速，随后进入匀速下落。打开伞的一瞬间阻力骤增，合力向上，人减速，然后在新的、小得多的终端速度上重新匀速。整个过程画成速度时间图就是一条先变陡后变平的曲线，开伞处速度突降再走水平线。很多学生在解释终端速度时只写阻力增大，漏掉阻力等于重力这一句。两分的解释题因此只拿到 1 分，写答案时按受力变化推速度变化才不会漏条件。
Air resistance grows with speed until it balances weight, the resultant force becomes zero and the object settles at terminal velocity; a skydiver accelerates first, then flows into a steady fall. The parachute opening raises drag sharply, so the resultant force points upwards, the person slows down and then falls again at a new and much lower steady speed. Plotted on a velocity-time graph this appears as a curve that flattens, a sudden drop and a horizontal line, and answers that never say the drag equals the weight pick up one mark out of two.
十一、牛顿第三定律与动量 / Newton's Third Law and Momentum
牛顿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、作用在不同物体上。因为它们作用在不同物体上，所以不会互相抵消，这一点是解释题的给分点。动量写成 p = mv，单位是 kg m/s，碰撞前后总动量相同。安全设计靠拉长碰撞时间降低力，由 F = dp/dt 可知同样的动量变化下时间越长、力越小。典型计算是 0.15 kg 的球以 20 m/s 撞墙后以 15 m/s 弹回，动量变化 5.25 kg m/s，接触 0.05 s 时平均力 105 N。学生最常把反作用力画在同一个物体上，受力图因此自相矛盾，另外弹回与停下算出的动量变化不同。
Newton's third law pairs equal and opposite forces that act on different objects, which is why they never cancel each other; momentum is mass times velocity in kg m/s and the total is conserved in a collision. Crumple zones, seat belts and airbags stretch the impact time, and since force is the change in momentum divided by the time taken, a longer contact time means a smaller force. A 0.15 kg ball arriving at 20 m/s and rebounding at 15 m/s changes momentum by 5.25 kg m/s, giving an average force of 105 N over 0.05 s.
十二、刹车距离与三周复习安排 / Stopping Distance and a Three-Week Plan
刹车距离是反应距离与制动距离之和，反应距离取决于反应时间与车速。制动距离取决于车速、质量、路面状况以及轮胎与刹车状态。英国交通部 Highway Code 给出的典型总距离约为 30 mph 时 23 m、60 mph 时 73 m。车速翻倍后距离增加远不止一倍，因为制动距离与速度的平方相关。反应时间受酒精、疲劳、药物与手机影响，这部分在 Edexcel 官方 spec 里属 Topic 1 的刹车距离条目。复习可以安排三周：第一周过公式与单位换算并各配两道计算题，第二周专攻两种图像与牛顿三定律的解释题。第三周做一整套 Paper 1 的限时练习，只看错题，把单位换算、图像面积与解释题漏条件这三类各写五道。
Stopping distance is thinking distance plus braking distance, where thinking distance depends on reaction time and speed while braking distance depends on speed, mass, road surface and the condition of the tyres and brakes; the Highway Code gives typical totals of about 23 m at 30 mph and 73 m at 60 mph. Because braking distance scales with the square of the speed, doubling the speed more than doubles the total distance. A three-week plan works well: refresh the equations and units, drill graph and explanation questions, then sit a timed Paper 1 and rewrite only the questions you missed.
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