📚 Speed and Velocity | 速率与速度
In CIE A-Level Physics, the distinction between speed and velocity is a fundamental idea that underpins kinematics. Although the two terms are often used interchangeably in everyday language, they carry precise physical meanings. Speed is a scalar quantity that measures how fast an object is moving, while velocity is a vector quantity that describes both how fast and in which direction the object travels. Understanding this difference is essential for interpreting motion graphs, solving vector problems, and answering exam questions accurately.
在 CIE A-Level 物理中，速率与速度的区分是支撑运动学的基本概念。虽然日常语言中这两个词经常互换使用，但它们在物理学中有严格的含义。速率是标量，描述物体运动有多快；速度是矢量，既描述快慢又描述运动方向。理解这一区别对于解读运动图像、求解矢量问题以及准确回答考试题目都至关重要。
1. Scalar and Vector Quantities | 标量与矢量
A scalar quantity has magnitude only. Speed is a scalar because it tells us the rate at which distance is covered, without any reference to direction. A vector quantity has both magnitude and direction. Velocity is a vector because it specifies the rate of change of displacement, which includes direction. Other scalar examples include mass, energy and temperature, while force, momentum and acceleration are vectors.
标量只有大小。速率是标量，因为它只说明距离随时间变化的快慢，不涉及方向。矢量既有大小又有方向。速度是矢量，因为它描述位移的变化率，而位移包含方向。其他标量例子包括质量、能量和温度；力、动量和加速度则是矢量。
2. Distance and Displacement | 距离与位移
To define speed and velocity clearly, we must first separate distance from displacement. Distance is the total length of the path travelled, regardless of direction. Displacement is the straight-line change in position from the starting point to the finishing point, together with its direction. If a runner completes one lap of a 400 m track, the distance travelled is 400 m, but the displacement is 0 m because the starting and finishing positions are identical.
要清晰定义速率和速度，必须先区分距离和位移。距离是物体运动路径的总长度，与方向无关。位移是从起点到终点的直线位置变化，并带有方向。如果一名跑步者绕 400 m 跑道跑完一圈，经过的距离是 400 m，但位移是 0 m，因为起点和终点位置相同。
3. Defining Speed | 速率的定义
Speed is defined as the distance travelled per unit time. It is calculated by dividing the total distance by the time taken. The SI unit of speed is metre per second, written m/s or m s⁻¹. In everyday situations, speed can also be expressed in kilometres per hour (km/h). To convert km/h to m/s, divide by 3.6. For example, 72 km/h equals 20 m/s.
速率定义为单位时间内通过的距离。它用总距离除以所用时间来计算。速率的国际单位是米每秒，写作 m/s 或 m s⁻¹。在日常生活中，速率也可以用千米每小时（km/h）表示。将 km/h 转换为 m/s 时，除以 3.6。例如，72 km/h 等于 20 m/s。
speed = total distance ÷ total time
4. Defining Velocity | 速度的定义
Velocity is defined as the displacement per unit time. Because displacement is a vector, velocity must also be a vector. It has the same direction as the displacement. Velocity is calculated by dividing the change in displacement by the time interval. Constant velocity requires both constant speed and constant direction. A car turning around a bend at a steady speed of 30 m/s does not have constant velocity because its direction is changing.
速度定义为单位时间内的位移。由于位移是矢量，速度也必须是矢量，其方向与位移方向相同。速度用位移的变化量除以时间间隔来计算。匀速运动要求速率和方向都保持不变。一辆汽车以 30 m/s 的稳定速率转弯时，速度并不恒定，因为方向正在改变。
velocity = Δdisplacement ÷ Δtime
5. Average Speed vs Average Velocity | 平均速率与平均速度
displacement is 20 km north, so the average velocity is 20 km north / 2 h = 10 km/h north.
平均速率和平均速度常常不同。平均速率使用总路径长度，而平均速度使用净位移。如果一辆汽车 1 小时内向北行驶 60 km，然后在 1 小时内向南行驶 40 km，平均速率为 (60 km + 40 km) / 2 h = 50 km/h。但净位移是向北 20 km，所以平均速度为 20 km 向北 / 2 h = 10 km/h 向北。
6. Instantaneous Speed and Velocity | 瞬时速率与瞬时速度
Instantaneous speed is the speed of an object at a particular moment in time. It is the magnitude of the instantaneous velocity. Instantaneous velocity is the rate of change of displacement at an instant, so it includes direction. In a distance-time graph, instantaneous speed is found from the gradient of the tangent to the curve. In a velocity-time graph, instantaneous velocity is simply read from the vertical axis at a given time.
瞬时速率是物体在某一特定时刻的速率，它是瞬时速度的大小。瞬时速度是某一瞬间位移的变化率，因此包含方向。在距离-时间图像中，瞬时速率由曲线切线的斜率得到。在速度-时间图像中，瞬时速度可直接从给定时间对应的纵轴读出。
7. Units and Conversions | 单位与换算
The SI unit for both speed and velocity is metre per second (m/s or m s⁻¹). Speeds in km/h are common in transport, so converting between units is a key skill. To convert km/h to m/s, multiply by 1000 and divide by 3600, which is the same as dividing by 3.6. To convert m/s to km/h, multiply by 3.6. A speed of 25 m/s is equivalent to 90 km/h. Always check whether a question expects SI units before substituting values.
速率和速度的国际单位都是米每秒（m/s 或 m s⁻¹）。交通运输中常用 km/h，因此单位换算是一项关键技能。将 km/h 转换为 m/s 时，先乘以 1000 再除以 3600，相当于除以 3.6。将 m/s 转换为 km/h 时乘以 3.6。25 m/s 的速率相当于 90 km/h。在代入数值前，一定要确认题目是否要求国际单位。
8. Distance-Time Graphs | 距离-时间图像
A distance-time graph plots distance on the vertical axis and time on the horizontal axis. The gradient of the graph gives the speed. A straight line indicates constant speed. A horizontal line indicates that the object is stationary. A curve indicates changing speed, and the gradient of the tangent at a point gives the instantaneous speed. Because distance never decreases, the graph never slopes downward.
距离-时间图像的纵轴表示距离，横轴表示时间。图像的斜率给出速率。直线表示匀速运动。水平线表示物体静止。曲线表示速率在变化，某点切线的斜率给出瞬时速率。由于距离不会减少，图像不会向下倾斜。
9. Displacement-Time and Velocity-Time Graphs | 位移-时间与速度-时间图像
A displacement-time graph can have positive and negative gradients. A positive gradient indicates motion in the chosen positive direction; a negative gradient indicates motion in the opposite direction. The gradient gives velocity. A velocity-time graph plots velocity against time. Its gradient gives acceleration, and the area under the graph between two times gives the displacement. A horizontal line on a velocity-time graph represents constant velocity.
位移-时间图像可以有正斜率和负斜率。正斜率表示物体沿选定的正方向运动，负斜率表示沿相反方向运动。斜率给出速度。速度-时间图像以速度为纵轴、时间为横轴。其斜率给出加速度，图像下两时刻之间的面积给出位移。速度-时间图像上的水平线表示匀速运动。
10. Common Misconceptions | 常见误区
Many students confuse speed with velocity and distance with displacement. A common error is to say that an object moving in a circle at constant speed has constant velocity. In fact, its velocity is changing because its direction is always changing. Another error is to treat negative velocity as 'slowing down'. Negative velocity simply means motion in the opposite direction; acceleration is needed to describe slowing down. Also, average speed is not always equal to the magnitude of average velocity.
许多学生混淆速率与速度，以及距离与位移。常见错误是认为物体以恒定速率做圆周运动时速度恒定。事实上，它的速度在不断变化，因为方向始终在改变。另一个错误是把负速度当作 '减速'。负速度只表示沿相反方向运动，减速需要加速度来描述。此外，平均速率并不总等于平均速度的大小。
11. Worked Example | 典型例题
The displacement is the straight-line distance from start to finish, found by Pythagoras: √6.0² + 8.0² = 10.0 m. The magnitude of average velocity = 10.0 m / 8.0 s = 1.25 m/s.
一名学生 3.0 s 内向东走 6.0 m，然后 5.0 s 内向北走 8.0 m。计算平均速率和平均速度的大小。总距离 = 6.0 m + 8.0 m = 14.0 m。总时间 = 8.0 s。平均速率 = 14.0 m / 8.0 s = 1.75 m/s。位移是从起点到终点的直线距离，由勾股定理求得：√6.0² + 8.0² = 10.0 m。平均速度大小 = 10.0 m / 8.0 s = 1.25 m/s。
12. Exam Tips for CIE | CIE 考试技巧
In CIE A-Level Physics, definitions must be precise. State that speed is a scalar quantity equal to distance per unit time, and velocity is a vector quantity equal to displacement per unit time. When a velocity answer is required, include both magnitude and direction. For graph questions, identify whether the y-axis represents distance, displacement or velocity before calculating gradients or areas. Show units in every step, and convert km/h to m/s when necessary. In extended questions, be ready to explain why an object with constant speed can still have changing velocity.
在 CIE A-Level 物理中，定义必须精确。要说明速率是标量，等于单位时间内的距离；速度是矢量，等于单位时间内的位移。当答案要求速度时，必须同时写出大小和方向。对于图像题，在计算斜率或面积之前，先确认纵轴表示的是距离、位移还是速度。每一步都要标明单位，必要时将 km/h 转换为 m/s。在扩展题中，要能解释为什么速率恒定的物体速度仍然可能变化。
Published by TutorHao | Physics Revision Series | aleveler.com
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