📚 Kinematics: Key Points for GCSE Edexcel Physics | GCSE Edexcel 物理：动力学考点精讲
Kinematics is a core topic in GCSE Edexcel Physics that deals with the description of motion. You need to understand scalars and vectors, speed, velocity, acceleration, distance-time graphs, velocity-time graphs, the equations of uniform acceleration, Newton's laws of motion, and practical measurement techniques. This article provides a complete revision guide to the key points that appear most often in exams, with clear definitions, formulas, graph interpretation rules, and common exam mistakes to avoid.
动力学是 GCSE Edexcel 物理中的核心主题，研究如何描述运动。你需要理解标量与矢量、速率、速度、加速度、距离-时间图像、速度-时间图像、匀加速运动方程、牛顿运动定律以及实验测量技巧。本文提供一份完整的考点精讲，涵盖考试中最常出现的定义、公式、图像判读规则和常见错误，帮助你有条理地复习。
1. Scalars and Vectors | 标量与矢量
In physics, quantities are divided into scalars and vectors. A scalar quantity has only magnitude, which means size or amount, and no direction. Distance, speed, mass, time, and energy, temperature, and power are all scalars.
在物理学中，物理量分为标量和矢量。标量只有大小，也就是只有量值或数量，没有方向。距离、速率、质量、时间、能量、温度和功率都是标量。
A vector quantity has both magnitude and direction. Displacement, velocity, acceleration, and force, weight, momentum, and electric field strength are vectors. A vector is not complete unless you state its direction.
矢量既有大小又有方向。位移、速度、加速度、力、重力、动量和电场强度都是矢量。一个矢量如果不说明方向，就是不完整的。
For example, saying "the car travels at 20 m/s" gives a scalar speed. Saying "the car travels at 20 m/s north" gives a vector velocity. The direction can be given as north, south, east, west, or as an angle, such as 30° above the horizontal.
例如，说"汽车以 20 m/s 行驶"给出的是标量速率。说"汽车以 20 m/s 向北行驶"给出的是矢量速度。方向可以用北、南、东、西表示，也可以用角度表示，例如与水平方向成 30°。
When you add vectors, direction matters. Two forces of 5 N and 3 N can produce a resultant of 8 N if they act in the same direction, 2 N if they act in opposite directions, or a value between 2 N and 8 N if they act at an angle. Scalar addition is simpler because only the sizes are added.
矢量相加时，方向很重要。5 N 和 3 N 两个力，如果方向相同，合力为 8 N；如果方向相反，合力为 2 N；如果成一定角度，合力介于 2 N 和 8 N 之间。标量相加更简单，因为只需要把大小相加。
Exam tip: always check whether the question asks for a scalar or a vector. If it asks for velocity, displacement, acceleration, or force, you must include direction and the correct unit.
考试提示：一定要看清题目问的是标量还是矢量。如果题目问速度、位移、加速度或力，你必须写出方向以及正确的单位。
2. Distance and Displacement | 距离与位移
Distance is the total length of the path travelled. It is a scalar, measured in metres (m), and it does not depend on direction. If you walk around a 400 m running track once, your distance is 400 m.
距离是物体经过路径的总长度。它是标量，单位为米（m），与方向无关。如果你绕 400 m 跑道走一圈，你的距离就是 400 m。
Displacement is the shortest straight-line distance from the starting point to the finishing point, together with the direction. It is a vector, also measured in metres, but it includes direction such as "50 m east".
位移是从起点到终点的直线距离，并带有方向。它是矢量，单位也是米，但需要包括方向，例如"向东 50 m"。
If you walk once around a 400 m track and finish where you started, your distance is 400 m but your displacement is 0 m. This is because the start and finish points are the same.
如果你绕 400 m 跑道走一圈，回到起点，你的距离是 400 m，但位移是 0 m。这是因为起点和终点相同。
Distance-time graphs always use distance or displacement on the vertical axis. In most GCSE Edexcel questions, the graph shows distance travelled, so the gradient gives speed rather than velocity. If the motion reverses direction, a displacement-time graph can go below the horizontal axis, but a distance-time graph cannot decrease unless the object is returning along the same path and distance is being measured as total path length.
距离-时间图像的纵轴使用距离或位移。在大多数 GCSE Edexcel 题目中，图像显示的是经过的距离，所以斜率表示速率而不是速度。如果运动反向，位移-时间图像可以降到横轴以下，但距离-时间图像通常不会下降，除非物体沿原路返回并且纵轴记录的是总路程。
A common exam question gives a journey with several stages and asks for total distance, total displacement, or average speed. Draw a simple sketch, label each stage, and keep directions as positive or negative if you are working with displacement.
常见考题会给出包含多个阶段的行程，要求计算总距离、总位移或平均速率。画一个简单草图，标出每一阶段；如果你处理的是位移，要把不同方向记为正或负。
3. Speed and Velocity | 速率与速度
Speed is the rate at which an object covers distance. It is a scalar and is can be calculated using the formula below.
速率是物体走过距离的快慢程度。它是标量，可用下面的公式计算。
speed = distance ÷ time
速率 = 距离 ÷ 时间
The SI unit of speed is metres per second, written as m/s. You may also see km/h or miles per hour in everyday situations. In physics calculations, convert km/h to m/s by dividing by 3.6, and convert m/s to km/h by multiplying by 3.6.
速率的国际单位是米每秒，写作 m/s。日常生活中也会见到 km/h 或英里每小时。在物理计算中，把 km/h 换算成 m/s 要除以 3.6，把 m/s 换算成 km/h 要乘以 3.6。
Average speed is the total distance travelled divided by the total time taken. It does not tell you what happens at each moment. Instantaneous speed is the speed at a particular instant, such as the reading on a car speedometer.
平均速率是总距离除以总时间。它不能说明每一时刻发生的情况。瞬时速率是某一瞬间的速率，例如汽车速度计上的读数。
Velocity is speed in a stated direction. It is a vector, so a change in direction is a change in velocity even if the speed stays constant. For example, a car moving around a roundabout at a steady 30 km/h is changing velocity because its direction is changing.
速度是带有方向的速率。它是矢量，所以即使速率不变，方向改变也意味着速度改变。例如，汽车以稳定的 30 km/h 绕环岛行驶，由于方向不断改变，它的速度也在改变。
The equation for average speed can be rearranged using the formula triangle.
平均速率公式可以用公式三角形来变形。
average speed = total distance ÷ total time
平均速率 = 总距离 ÷ 总时间
If a journey has several stages, calculate the total distance and total time separately before dividing. Do not average the speeds unless the times for each stage are equal. This is one of the most common mistakes in GCSE Edexcel kinematics questions.
如果一段行程有多个阶段，要先分别计算总距离和总时间，再做除法。除非各阶段所用时间相等，否则不能直接把速率取平均。这是 GCSE Edexcel 动力学题目中最常见的错误之一。
4. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector measured in metres per second squared, written as m/s². An object accelerates when its speed changes, its direction changes, or both change.
加速度是速度的变化率。它是矢量，单位为米每二次方秒，写作 m/s²。当物体的速率改变、方向改变，或两者都改变时，物体就在加速。
acceleration = change in velocity ÷ time taken
加速度 = 速度变化量 ÷ 所用时间
a = Δv ÷ t
a = (v − u) ÷ t
itial velocity, v is the final velocity, and t is the time taken. The change in velocity is v − u. If the final velocity is smaller than the initial velocity, the acceleration is negative, which is often called deceleration or retardation.
在公式 a = (v − u) ÷ t 中，u 是初速度，v 是末速度，t 是所用时间。速度变化量是 v − u。如果末速度小于初速度，加速度为负值，通常称为减速或阻滞。
6 m/s, so a = 6 ÷ 3 = 2 m/s². This means the cyclist gains 2 m/s of velocity every second.
示例：一名自行车手在 3 s 内速度从 4 m/s 增加到 10 m/s。速度变化量为 10 − 4 = 6 m/s，所以 a = 6 ÷ 3 = 2 m/s²。这表示自行车手每秒钟速度增加 2 m/s。
Do not confuse acceleration with speed. A car can have a very high speed and zero acceleration if it is travelling at a constant velocity. A car can also have a high acceleration at a low speed, such as when it first starts moving.
不要把加速度和速率混淆。汽车可以速率很高但加速度为零，如果它做匀速运动。汽车也可以在速率很低时加速度很大，例如刚启动时。
5. Distance-Time Graphs | 距离-时间图像
A distance-time graph plots distance travelled on the vertical axis and time on the horizontal axis. The gradient of the graph gives the speed of the object. A steeper gradient means a higher speed.
距离-时间图像把经过的距离画在纵轴，把时间画在横轴。图像的斜率表示物体的速率。斜率越陡，速率越大。
A horizontal line means the object is stationary, because the distance is not changing as time passes. A straight line sloping upwards means constant speed. A curve that gets steeper means the object is accelerating. A curve that gets less steep means the object is decelerating.
水平线表示物体静止，因为距离不随时间改变。向上倾斜的直线表示匀速运动。越来越陡的曲线表示物体在加速。越来越平缓的曲线表示物体在减速。
speed = gradient = change in distance ÷ change in time
速率 = 斜率 = 距离变化量 ÷ 时间变化量
To find the gradient, choose two points on the line that are far apart, draw a right-angled triangle, and divide the vertical change by the horizontal change. Always include units in your answer, such as m/s.
求斜率时，在直线上选择相距较远的两点，画一个直角三角形，用竖直变化量除以水平变化量。答案一定要带单位，例如 m/s。
If the graph shows displacement rather than distance, a negative gradient means the object is moving in the opposite direction. On a distance-time graph, the line normally does not go below zero because distance is a scalar and cannot be negative.
如果图像显示的是位移而不是距离，负斜率表示物体朝相反方向运动。在距离-时间图像中，线通常不会低于零，因为距离是标量，不能为负。
Exam tip: read the axes carefully. A common trap is a graph labelled "distance-time" but with displacement values. Check whether the question asks for speed or velocity before you calculate the gradient.
考试提示：仔细阅读坐标轴。常见陷阱是图像标为"距离-时间"，但数据其实是位移。计算斜率前先确认题目问的是速率还是速度。
6. Velocity-Time Graphs | 速度-时间图像
A velocity-time graph plots velocity on the vertical axis and time on the horizontal axis. The gradient of a velocity-time graph gives acceleration. A positive gradient means acceleration, a negative gradient means deceleration, and a zero gradient means constant velocity.
速度-时间图像把速度画在纵轴，把时间画在横轴。速度-时间图像的斜率表示加速度。正斜率表示加速，负斜率表示减速，零斜率表示匀速运动。
acceleration = gradient = change in velocity ÷ change in time
加速度 = 斜率 = 速度变化量 ÷ 时间变化量
The area under a velocity-time graph gives the distance travelled. For a straight-line graph, split the area into triangles and rectangles, calculate each area, and add them together. Remember that area below the horizontal axis represents motion in the opposite direction.
速度-时间图像下方的面积表示经过的距离。对于直线图像，把面积分成三角形和长方形，分别计算后相加。记住横轴以下的面积表示朝相反方向运动。
− 0) ÷ 6 = 2 m/s². The distance travelled is the area of the triangle: ½ × 6 × 12 = 36 m.
示例：速度-时间图像显示一条直线，从 0 s 时的 0 m/s 到 6 s 时的 12 m/s。加速度为 (12 − 0) ÷ 6 = 2 m/s²。经过的距离是三角形面积：½ × 6 × 12 = 36 m。
ary. On a velocity-time graph, gradient = acceleration and a horizontal line = constant velocity.
比较距离-时间图像和速度-时间图像是常见考题。在距离-时间图像中，斜率 = 速率，水平线 = 静止。在速度-时间图像中，斜率 = 加速度，水平线 = 匀速运动。
| Graph type | Gradient gives | Area under graph gives |
| Distance-time | Speed | No physical meaning at GCSE |
| Velocity-time | Acceleration | Distance travelled |
| 图像类型 | 斜率表示 | 图像下面积表示 |
| 距离-时间 | 速率 | GCSE 阶段无物理意义 |
| 速度-时间 | 加速度 | 经过的距离 |
7. Equations of Uniform Acceleration | 匀加速运动方程
When an object moves with uniform acceleration, its acceleration is constant. GCSE Edexcel Physics uses a set of equations that relate initial velocity u, final velocity v, acceleration a, distance s, and time t.
当物体做匀加速运动时，它的加速度是恒定的。GCSE Edexcel 物理使用一组方程，把初速度 u、末速度 v、加速度 a、距离 s 和时间 t 联系起来。
v = u + at
s = (u + v) ÷ 2 × t
v² = u² + 2as
s = ut + ½at²
These four equations are sometimes called the SUVAT equations, because they use the symbols s, u, v, a, and t. You do not need to memorise every derivation, but you must be able to choose the correct equation and rearrange it accurately.
这四个方程有时称为 SUVAT 方程，因为它们使用 s、u、v、a、t 这几个符号。你不需要记住每个推导过程，但必须能够选择正确的方程并准确变形。
you need a, use v² = u² + 2as. If you know u, a, and t and you need s, use s = ut + ½at².
选择正确方程的方法是：列出已知量和要求的量。例如，如果已知 u、v 和 s，要求 a，就用 v² = u² + 2as。如果已知 u、a 和 t，要求 s，就用 s = ut + ½at²。
t gives v = 0 + 3 × 5 = 15 m/s. Using s = ut + ½at² gives s = 0 × 5 + ½ × 3 × 5² = 37.5 m.
示例：汽车从静止开始以 3 m/s² 加速 5 s。用 v = u + at 得 v = 0 + 3 × 5 = 15 m/s。用 s = ut + ½at² 得 s = 0 × 5 + ½ × 3 × 5² = 37.5 m。
Always check the signs. If the object is slowing down, a is negative. If the object is moving in the opposite direction, u or v may be negative. Marks are often lost because students forget to include the negative sign.
一定要检查正负号。如果物体在减速，a 为负值。如果物体朝相反方向运动，u 或 v 可能为负值。学生经常因为忘记负号而丢分。
8. Newton's Laws of Motion | 牛顿运动定律
Newton's first law states that an object remains at rest or moves at constant velocity unless acted upon by a resultant force. This is why a book stays on a table and why a spacecraft can travel at constant speed in deep space without using fuel.
牛顿第一定律指出，如果没有合力作用，物体保持静止或匀速直线运动。这就是为什么书会停在桌面上，也是为什么航天器在深空中可以不消耗燃料而保持恒定速度。
Newton' quation is F = m × a, where F is the resultant force in newtons, m is mass in kilograms, and a is acceleration in m/s².
牛顿第二定律指出，物体的加速度与合力成正比，与质量成反比。公式为 F = m × a，其中 F 是合力，单位为牛顿；m 是质量，单位为千克；a 是加速度，单位为 m/s²。
F = m × a
合力 = 质量 × 加速度
Newton's third law states that for every action force, there is an equal and opposite reaction force. The two forces act on different objects, so they do not cancel out. For example, when you push a wall, the wall pushes back on you with the same size force in the opposite direction.
牛顿第三定律指出，每一个作用力都有一个大小相等、方向相反的反作用力。这两个力作用在不同的物体上，所以不会相互抵消。例如，你推墙时，墙也以大小相同、方向相反的力推你。
A common exam mistake is to think that action and reaction forces cancel. They do not, because they act on different objects. A resultant force of zero only occurs when forces act on the same object and cancel.
常见考试错误是认为作用力和反作用力会抵消。它们不会，因为它们作用在不同物体上。只有当力作用在同一物体上并相互抵消时，合力才为零。
9. Mass, Weight and Resultant Force | 质量、重力与合力
Mass is the amount of matter in an object. It is a scalar measured in kilograms (kg) and does not change with location. Weight is the force of gravity acting on an object. It is a vector measured in newtons (N) and depends on the gravitational field strength g.
质量是物体所含物质的多少。它是标量，单位为千克（kg），不随位置改变。重力是地球对物体的引力。它是矢量，单位为牛顿（N），取决于重力场强度 g。
weight = mass × gravitational field strength
W = m × g
On Earth, g is about 9.8 N/kg, which is often rounded to 10 N/kg in GCSE calculations. On the Moon, g is about 1.6 N/kg, so an astronaut has the same mass but a much smaller weight.
在地球上，g 约为 9.8 N/kg，在 GCSE 计算中常取 10 N/kg。在月球上，g 约为 1.6 N/kg，所以航天员的质量不变，但重力小得多。
The resultant force is the single force that has the same effect as all the forces acting on an object combined. If the resultant force is zero, the object stays at rest or moves at constant velocity. If the resultant force is not zero, the object accelerates in the direction of the resultant force.
合力是与作用在物体上的所有力共同效果相同的单一力。如果合力为零，物体保持静止或匀速运动。如果合力不为零，物体就沿合力方向加速。
the box has a mass of 4 kg, its acceleration is a = F ÷ m = 12 ÷ 4 = 3 m/s² to the right.
示例：箱子受到向右 20 N 的推力，摩擦力向左 8 N。合力为向右 20 − 8 = 12 N。如果箱子质量为 4 kg，其加速度为 a = F ÷ m = 12 ÷ 4 = 3 m/s²，方向向右。
Always draw a free-body diagram before solving force problems. Label each force with its size, unit, and direction. This makes it much easier to find the resultant force and avoids sign errors.
解决力学问题前一定要画受力图。标出每个力的大小、单位和方向。这样更容易求合力，也能避免正负号错误。
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