WJEC物理 运动学 加速度 牛顿定律 图像题
运动学是 WJEC GCSE Physics 里承上启下的板块:它既用简单的数学描述物体的运动,又为牛顿定律、力与加速度的关系打基础。在威尔斯考试局的试卷中,这部分内容主要出现在 Unit 2(Forces, Space and Radioactivity),题型以计算题和读图题为主,分值占比不低。这篇入门文章把速度、加速度、两种运动图像和牛顿三大定律一次讲清楚,并配上真题风格练习。
Kinematics is a connecting topic in WJEC GCSE Physics. It uses simple mathematics to describe how objects move, and it lays the foundation for Newton's laws and the link between force and acceleration. In the Welsh exam board's papers, most of this content appears in Unit 2 (Forces, Space and Radioactivity), where questions are mainly calculations and graph reading. This beginner guide explains speed, acceleration, the two motion graphs and Newton's three laws clearly, with exam style practice at the end.
一、距离、速度与加速度的基础概念
先分清三组易混词。距离 distance 是物体实际走过的路径总长,只有大小没有方向,属于标量 scalar;位移 displacement 是起点到终点的直线距离,带方向,属于矢量 vector。速度 speed 对应距离,表示单位时间内走了多远;速率 velocity 对应位移,必须说明方向。公式都是 v = s / t,单位是米每秒 m/s。加速度 acceleration 表示速度变化的快慢,公式 a = (v - u) / t,其中 u 是初速度,v 是末速度,t 是所用时间,单位是米每二次方秒 m/s²。
First, keep three confusing pairs apart. Distance is the total length of the path actually travelled; it has size only and is a scalar. Displacement is the straight line distance from start to finish and carries a direction, so it is a vector. Speed is distance divided by time and tells you how far an object travels each second, while velocity is displacement divided by time and must state a direction. Both use v = s / t with the unit metres per second, m/s. Acceleration measures how quickly velocity changes, using a = (v - u) / t, where u is initial velocity, v is final velocity and t is the time taken. Its unit is metres per second squared, m/s².
例题:短跑选手用 12.5 秒跑完 100 米,平均速度是多少?直接用 v = s / t = 100 / 12.5 = 8.0 m/s。注意平均速度不等于瞬时速度,选手冲刺瞬间可能超过 10 m/s。考试时先写公式、再代入数字、最后写单位,三步齐全才能拿满计算分。
Worked example: a sprinter runs 100 m in 12.5 s. The average speed is v = s / t = 100 / 12.5 = 8.0 m/s. Note that average speed is not the instantaneous speed; the sprinter may exceed 10 m/s at the finish. In the exam, write the formula first, then substitute the numbers, then give the unit. All three steps are needed for full marks on a calculation.
二、加速度计算与减速
加速度为正值表示速度越来越大,负值表示速度越来越小,这时通常叫减速 deceleration。计算减速时,把末速度放在初速度前面相减,结果自然是负数。做题最常见的错误是把单位搞混:题目给 km/h 时,要先除以 3.6 换成 m/s,例如 54 km/h = 54 / 3.6 = 15 m/s,因为 1 m/s = 3.6 km/h。
A positive acceleration means the object is speeding up, while a negative value means it is slowing down, which is usually called deceleration. When calculating deceleration, subtract the final velocity from the initial velocity and the answer is naturally negative. The most common mistake is mixing up units. When a question gives km/h, divide by 3.6 to convert to m/s first, because 1 m/s = 3.6 km/h. For example 54 km/h = 54 / 3.6 = 15 m/s.
例题:一辆自行车在 4 秒内从 6 m/s 匀加速到 18 m/s,加速度多大?代入 a = (v - u) / t = (18 - 6) / 4 = 3 m/s²。若同样在 4 秒内从 18 m/s 刹停,加速度为 a = (0 - 18) / 4 = -4.5 m/s²,负号表示方向与运动方向相反,答题时描述为以 4.5 m/s² 减速即可。
Worked example: a bicycle accelerates uniformly from 6 m/s to 18 m/s in 4 s. Using a = (v - u) / t = (18 - 6) / 4 gives 3 m/s². If it then stops from 18 m/s in 4 s, a = (0 - 18) / 4 = -4.5 m/s². The negative sign shows the acceleration acts opposite to the direction of motion, so you can describe it simply as a deceleration of 4.5 m/s².
三、距离-时间图像 Distance-Time Graphs
距离-时间图像横轴是时间,纵轴是离起点的距离,图像上某点的斜率 gradient 就是该时刻的速度。斜线越陡,速度越大;水平线表示物体静止;斜线向下走表示物体往回运动。读图题常问:哪个阶段速度最大?比较各段斜率即可,不必计算。
On a distance-time graph the horizontal axis is time and the vertical axis is distance from the start. The gradient of the line at any point is the speed at that moment. A steeper slope means a larger speed, a horizontal line means the object is stationary, and a downward slope means it is returning towards the start. A common question asks which stage has the greatest speed; compare the slopes and you do not need to calculate.
计算示例:某学生步行,前 20 秒走了 40 米,然后休息 10 秒,再用 30 秒走回起点。第一段速度 = 40 / 20 = 2 m/s;休息段斜率为 0,速度为零;回程段位移为 -40 米(方向相反),速度大小 = 40 / 30 约等于 1.3 m/s。画图时注意休息段一定是水平线,不能画成斜线。
Calculation example: a student walks 40 m in the first 20 s, rests for 10 s, then walks back to the start in 30 s. The first stage speed is 40 / 20 = 2 m/s. The resting stage has zero gradient, so the speed is zero. On the return the displacement is -40 m because the direction is reversed, and the speed is 40 / 30, about 1.3 m/s. When drawing the graph, the rest stage must be a horizontal line, never a slope.
四、速度-时间图像 Velocity-Time Graphs
速度-时间图像是本单元最重要的图像,读法比距离-时间图像多两层:第一,斜率表示加速度,斜线越陡加速度越大,水平线表示匀速运动,斜率为负表示减速;第二,图线与横轴围成的面积 area under the graph 表示这段时间内走过的距离。这两条规则是 WJEC 计算题的高频考点。
The velocity-time graph is the most important graph in this unit and needs two extra reading rules. First, the gradient represents acceleration: a steeper slope means a larger acceleration, a horizontal line means constant velocity, and a negative slope means deceleration. Second, the area between the line and the time axis equals the distance travelled in that interval. These two rules are frequent targets of WJEC calculation questions.
计算示例:一辆车从静止匀加速,5 秒后达到 20 m/s,再匀速行驶 10 秒,最后用 4 秒刹停。加速度段斜率 = 20 / 5 = 4 m/s²。总距离 = 三角形面积 + 矩形面积 + 三角形面积 = (0.5 × 5 × 20) + (10 × 20) + (0.5 × 4 × 20) = 50 + 200 + 40 = 290 m。三角形面积公式 二分之一底乘高 必须记住,读图时先把图形拆成三角形和矩形再分别求面积。
Calculation example: a car accelerates uniformly from rest to 20 m/s in 5 s, travels at constant velocity for 10 s, then brakes to a stop in 4 s. The gradient of the first stage is 20 / 5 = 4 m/s². The total distance is triangle area plus rectangle area plus triangle area = (0.5 × 5 × 20) + (10 × 20) + (0.5 × 4 × 20) = 50 + 200 + 40 = 290 m. Learn the triangle area formula, half base times height, and split any graph into triangles and rectangles before finding each area.
五、牛顿三大定律 Newton's Laws of Motion
牛顿第一定律:物体在不受外力或所受合力为零时,保持静止或匀速直线运动状态,直到有外力改变它。这解释了惯性 inertia:质量越大的物体越难改变运动状态,所以载重卡车比小汽车更难刹停。安全带 seat belt 和安全气囊就是利用第一定律设计的,急刹车时人体仍想保持前进,安全带把人拉住,防止撞向仪表盘。
Newton's first law states that an object stays at rest or moves at constant velocity unless a resultant force acts on it. This is linked to inertia: the larger the mass, the harder it is to change the object's motion, which is why a loaded lorry is much harder to stop than a car. Seat belts and air bags are designed around this law. During a sudden stop your body still wants to keep moving forward, and the belt holds you back from hitting the dashboard.
牛顿第二定律给出力与加速度的数量关系:F = ma,合力 F 的单位是牛顿 N,质量 m 的单位是千克 kg,加速度 a 的单位是 m/s²。例题:一辆 1200 kg 的汽车以 2.5 m/s² 加速,需要的合力 = 1200 × 2.5 = 3000 N。重力是常见的力,物体重量 W = mg,其中 g 取 10 N/kg(精确值约 9.8 N/kg),所以 60 kg 的学生重量约为 600 N。
Newton's second law gives the quantitative link between force and acceleration: F = ma, where the resultant force F is in newtons, mass m is in kilograms and acceleration a is in m/s². Example: a 1200 kg car accelerates at 2.5 m/s², so the resultant force needed is 1200 × 2.5 = 3000 N. Weight is the most familiar force. An object's weight is W = mg, where g is about 10 N/kg (more precisely 9.8 N/kg), so a 60 kg student has a weight of roughly 600 N.
牛顿第三定律:作用力和反作用力大小相等、方向相反,作用在不同物体上。火箭向后喷出气体,气体给火箭一个向前的推力,就是典型的第三定律例子。考试常设陷阱:把第三定律误写成平衡力。区别在于平衡力作用在同一个物体上,而作用力与反作用力作用在两个不同的物体上。
Newton's third law states that every action has an equal and opposite reaction, and the two forces act on different objects. A rocket pushes exhaust gases backwards and the gases push the rocket forwards, a classic example. Exams often set a trap here: confusing action-reaction pairs with balanced forces. The difference is that balanced forces act on the same object, while an action-reaction pair acts on two different objects.
六、质量与重量、制动距离考点
质量 mass 是物体所含物质的多少,单位 kg,不随地点改变;重量 weight 是地球对物体的引力,单位 N,随地点改变。同一物体在月球上质量不变,但重量约为地球的六分之一。太空中的宇航员处于失重状态,感觉不到重量,但质量没有变,因此推同一个箱子仍然要用同样的力。
Mass is the amount of matter in an object, measured in kg, and it does not change with location. Weight is the gravitational pull on the object, measured in N, and it does change with location. The same object keeps its mass on the Moon but weighs about one sixth of its Earth weight. An astronaut in orbit feels weightless, yet the mass is unchanged, so pushing the same box still needs the same force.
制动距离 stopping distance 包括思考距离 thinking distance 和刹车距离 braking distance 两部分。思考距离取决于反应时间,酒精、疲劳和手机都会延长反应时间;刹车距离取决于车速和质量。速度加倍,刹车距离大约变成四倍,因为动能与速度的平方成正比。这也是限速和保持车距的物理依据,属于 WJEC 常考的应用题素材。
Stopping distance has two parts: thinking distance and braking distance. Thinking distance depends on reaction time, which alcohol, tiredness and phones all lengthen. Braking distance depends on speed and mass. If speed doubles, the braking distance roughly quadruples, because kinetic energy is proportional to the square of speed. This is the physics behind speed limits and safe following distances, and WJEC often uses it in application questions.
七、高频易错点
易错点一:单位换算漏除 3.6,km/h 直接代入公式,导致答案偏大 3.6 倍。易错点二:混淆两种图像,把距离-时间图像的斜率当成加速度,把速度-时间图像的斜率当成速度。记住口诀:距离图看斜率得速度,速度图看斜率得加速度、看面积得距离。易错点三:矢量方向表述不全,题目问 velocity 时必须写清方向。
Mistake one: forgetting to divide by 3.6, so km/h values are substituted directly and the answer comes out 3.6 times too large. Mistake two: confusing the two graphs, treating the slope of a distance-time graph as acceleration or the slope of a velocity-time graph as speed. Remember the rule: on a distance-time graph the slope gives speed; on a velocity-time graph the slope gives acceleration and the area gives distance. Mistake three: leaving out direction when asked for velocity, which is a vector.
易错点四:面积算错,忘记把图形拆成三角形和矩形,或者底和高取错线段。易错点五:牛顿第三定律与平衡力混淆。易错点六:重量单位写成 kg,重量是力,单位必须是 N。检查方法:答完每道计算题后回读一遍,确认公式、代入、单位、方向四个要素都齐全,可稳定减少失分。
Mistake four: area errors, such as not splitting the graph into triangles and rectangles or reading the wrong base and height. Mistake five: mixing up action-reaction pairs with balanced forces. Mistake six: writing weight in kg; weight is a force, so its unit must be N. A useful habit is to reread every calculation and check that the formula, substitution, unit and direction are all present, which reliably cuts lost marks.
八、真题演练 Exam Style Questions
题目一(1 分):一辆玩具车以 3 m/s 匀速行驶 20 秒,它走了多远?答案:s = v × t = 3 × 20 = 60 m。答:60 m。解题关键是先判断是匀速,直接套用距离等于速度乘时间。
Question 1, 1 mark: a toy car moves at a steady 3 m/s for 20 s. How far does it travel? Answer: s = v × t = 3 × 20 = 60 m. The key is recognising uniform motion and applying distance equals speed multiplied by time.
题目二(2 分):一辆摩托车从静止开始,5 秒内匀加速到 25 m/s,求加速度。答案:a = (v - u) / t = (25 - 0) / 5 = 5 m/s²。得 2 分的写法是列出公式并代入,最后给出带单位的答案。
Question 2, 2 marks: a motorcycle accelerates uniformly from rest to 25 m/s in 5 s. Find its acceleration. Answer: a = (v - u) / t = (25 - 0) / 5 = 5 m/s². The two-mark layout is formula, substitution and a final answer with its unit.
题目三(4 分):速度-时间图像显示一辆车 6 秒内从 0 匀加速到 30 m/s,之后匀速 4 秒,再用 3 秒刹停。(a)求最大加速度;(b)求总行驶距离。答案:(a)第一阶段斜率 = 30 / 6 = 5 m/s²;(b)总距离 = (0.5 × 6 × 30) + (4 × 30) + (0.5 × 3 × 30) = 90 + 120 + 45 = 255 m。这类综合题先标出三段,再逐段用面积公式,最后相加。
Question 3, 4 marks: a velocity-time graph shows a car accelerating uniformly from 0 to 30 m/s in 6 s, travelling steadily for 4 s, then braking to a stop in 3 s. (a) Find the maximum acceleration. (b) Find the total distance travelled. Answers: (a) the first stage gradient is 30 / 6 = 5 m/s²; (b) total distance = (0.5 × 6 × 30) + (4 × 30) + (0.5 × 3 × 30) = 90 + 120 + 45 = 255 m. For such questions label the three stages first, apply the area formula to each, then add them together.
九、关键双语术语
Distance 距离 | Displacement 位移 | Speed 速率 | Velocity 速度 | Acceleration 加速度 | Deceleration 减速 | Scalar 标量 | Vector 矢量 | Gradient 斜率 | Uniform acceleration 匀加速 | Inertia 惯性 | Mass 质量 | Weight 重量 | Resultant force 合力 | Thinking distance 思考距离 | Braking distance 刹车距离 | Stopping distance 制动距离 | Area under the graph 图像面积。考前把这一列术语过一遍,读题速度和准确率都会明显提升。
Run through these terms before the exam: distance, displacement, speed, velocity, acceleration, deceleration, scalar, vector, gradient, uniform acceleration, inertia, mass, weight, resultant force, thinking distance, braking distance, stopping distance, and area under the graph. Knowing them well improves both reading speed and accuracy in the exam.
Cambridge International AS ALevel Physics Coursebook 正版剑桥国际AS ALevel考试物理教材带线上账号 英文原版¥557.0📱 去京东购买京东精选
A-Level / GCSE / IB / KS2-KS3 全科辅导,中英双语教学
一对一辅导 考前冲刺 免费试听
Visit aleveler.com
或截图后用「扫一扫 → 相册」选择本图