Motion and Kinematics | 运动学基础

📚 Motion and Kinematics | 运动学基础

This revision note covers the core ideas in the Cambridge IGCSE Science / Physics topic of Motion: how to describe movement using scalar and vector quantities, distance, displacement, speed, velocity, acceleration, and how to interpret distance-time and speed-time graphs. Understanding these tools allows you to analyse everyday motion and solve examination problems confidently.

本复习讲义涵盖剑桥 IGCSE 科学 / 物理“运动”章节的核心内容：如何用标量和矢量、路程、位移、速率、速度、加速度来描述运动，以及如何解读距离-时间图和速度-时间图。掌握这些工具能帮助你分析日常运动现象，并从容解答考试题目。

1. Scalar and Vector Quantities | 标量与矢量

In physics, measurements are classified as scalar or vector. A scalar quantity has magnitude only, such as distance, speed, time, mass and energy. A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration and force.

在物理中，测量量分为标量和矢量。标量只有大小，例如路程、速率、时间、质量和能量。矢量既有大小又有方向，例如位移、速度、加速度和力。

When you describe motion, always check whether a direction is needed. Saying ‘the car moved 100 m’ gives distance, but saying ‘the car moved 100 m north’ gives displacement. Saying ‘the car moved at 20 m/s’ gives speed, but adding a direction gives velocity.

描述运动时，要始终判断是否需要说明方向。说“汽车移动了100 m”给出的是路程，而说“汽车向北移动了100 m”给出的是位移。说“汽车以20 m/s运动”给出的是速率，加上方向才是速度。

A vector can be represented by an arrow: the length of the arrow shows magnitude and the arrowhead shows direction. When vectors act along a straight line, you add them if they point in the same direction and subtract them if they point in opposite directions.

矢量可以用箭头表示：箭头的长度表示大小，箭尖表示方向。当矢量沿同一直线作用时，如果方向相同则相加，如果方向相反则相减。

• Scalar examples: distance, speed, time, mass, energy
• Vector examples: displacement, velocity, acceleration, force

2. Distance and Displacement | 路程与位移

Distance is the total length of the path travelled by an object. It does not depend on direction, so distance is always positive and cannot decrease. Displacement is the straight-line distance from the starting point to the finishing point in a specified direction.

路程是物体运动轨迹的总长度。它与方向无关，因此路程总是正值且不会减少。位移是从起点到终点的直线距离，并带有明确方向。

For example, if an athlete runs once around a 400 m track, the distance travelled is 400 m, but the displacement is 0 m because the starting and finishing positions are the same. If a person walks 3 km east and then 4 km west, the distance is 7 km but the displacement is only 1 km west.

例如，如果运动员绕400 m跑道跑一圈，运动路程为400 m，但位移为0 m，因为起点和终点位置相同。如果一个人先向东走3 km，再向西走4 km，则路程为7 km，但位移仅为向西1 km。

Displacement is often expressed with a direction such as north, south, east, west, or as an angle measured from a reference direction. In calculations, always state the direction of a displacement if it is not zero.

位移通常用方向表示，例如北、南、东、西，或者用与参考方向的夹角表示。在计算中，如果位移不为零，一定要说明其方向。

3. Speed and Velocity | 速率与速度

Speed is the rate at which distance is covered. It is calculated as speed = distance ÷ time. Velocity is the rate of change of displacement, so velocity = displacement ÷ time. Both can be measured in metres per second, m/s.

速率是路程随时间变化的快慢，计算公式为 速率 = 路程 ÷ 时间。速度是位移随时间变化的快慢，因此 速度 = 位移 ÷ 时间。两者的单位都可以是米每秒，m/s。

Average speed ignores any changes during the journey: average speed = total distance ÷ total time. Instantaneous speed is the speed at a particular moment, read from a speedometer or the gradient of a distance-time graph at that instant.

平均速率不考虑运动过程中的变化：平均速率 = 总路程 ÷ 总时间。瞬时速率是某一时刻的速率，可从速度表读出，或由距离-时间图在该时刻的斜率求得。

v = Δd ÷ Δt

To convert from kilometres per hour to metres per second, divide by 3.6. For example, 72 km/h = 72 ÷ 3.6 = 20 m/s. To convert from m/s to km/h, multiply by 3.6.

将千米每小时转换为米每秒时，除以3.6。例如，72 km/h = 72 ÷ 3.6 = 20 m/s。将 m/s 转换为 km/h 时，乘以3.6。

Typical everyday speeds include a person walking at about 1.5 m/s, a cyclist at about 5 m/s, and a car on a motorway at about 30 m/s. These values are useful for estimating and checking answers.

日常典型速率包括：人步行约为1.5 m/s，骑自行车约为5 m/s

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