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Motion of a Particle in a Straight Line | 质点直线运动

2026-08-30 01:18 · 本文部分内容由AI辅助创作

📚 Motion of a Particle in a Straight Line | 质点直线运动

Kinematics in a straight line is one of the most rewarding topics in the Edexcel IGCSE Mathematics syllabus. It connects algebra, graphs and real-world physical intuition, and once you master the core ideas — displacement, velocity, acceleration, and the SUVAT equations — you will be able to solve a wide range of examination questions with confidence.

直线运动是爱德思 IGCSE 数学考纲中最有价值的专题之一。它将代数、图像与真实世界的物理直觉联系起来。一旦掌握了核心概念——位移、速度、加速度以及 SUVAT 方程——你就能从容应对考试中各种相关问题。

1. Displacement and Distance | 位移与路程

A particle moving in a straight line has its position described by its displacement. Displacement is a vector quantity: it tells us both how far the particle is from a chosen origin and in which direction. Distance, by contrast, is a scalar quantity — it measures the total length of the path travelled, ignoring direction.

沿直线运动的质点，其位置由位移来描述。位移是矢量：它既告诉我们质点离选定原点有多远，也告诉我们方向。相比之下，路程是标量——它只衡量运动路径的总长度，不考虑方向。

For example, a particle that moves 3 m to the right and then 4 m back to the left has a total distance of 7 m, but its displacement from the start is only 1 m to the left (or −1 m if right is taken as positive).

例如，一个质点先向右运动 3 米，再向左返回 4 米，其总路程为 7 米，但相对起点的位移仅为向左 1 米（若规定向右为正，则为 −1 米）。

In straight-line motion, we typically choose a positive direction (often to the right or upward). Displacements in that direction are positive; displacements opposite to it are negative. This sign convention is critical throughout kinematics.

在直线运动中，我们通常选定一个正方向（常取向右或向上）。沿该方向的位移为正，相反方向的位移为负。这个正负号约定在运动学中贯穿始终，至关重要。

2. Velocity and Speed | 速度与速率

Velocity is the rate of change of displacement with respect to time. It is a vector, so it includes direction. Speed, on the other hand, is the rate of change of distance — it is a scalar. Both are measured in metres per second (m s⁻¹ or m/s).

速度是位移对时间的变化率，是矢量，包含方向。而速率是路程对时间的变化率，是标量。两者的单位均为米每秒（m s⁻¹ 或 m/s）。

Average velocity is defined as displacement divided by the time taken. Average speed is total distance divided by total time. A particle completing a round trip back to its starting point has zero average velocity but a non-zero average speed.

平均速度定义为位移除以所用时间；平均速率定义为总路程除以总时间。一个质点做完一次往返运动回到起点时，平均速度为零，但平均速率不为零。

Instantaneous velocity is the velocity at a particular instant — it equals the gradient of the displacement–time graph at that moment.

瞬时速度是某一时刻的速度，它等于位移—时间图像上该时刻的切线斜率。

For straight-line motion with constant velocity v, the displacement after time t is:

在匀速直线运动中，经过时间 t 后的位移为：

s = vt

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3. Acceleration | 加速度

Acceleration is the rate of change of velocity. It is measured in metres per second squared (m s⁻²). A positive acceleration means the velocity is increasing in the chosen positive direction; a negative acceleration (often called deceleration) means the velocity is decreasing.

加速度是速度的变化率，单位为米每二次方秒（m s⁻²）。正加速度表示速度沿所选正方向增大；负加速度（通常称为减速度）表示速度在减小。

For constant acceleration a over a time interval t, where u is the initial velocity and v is the final velocity:

对于匀加速运动，在时间间隔 t 内，设 u 为初速度、v 为末速度：

a = (v − u) ÷ t

In the Edexcel IGCSE syllabus, we focus entirely on constant acceleration. When acceleration is not constant, calculus would be required, which is beyond this level.

爱德思 IGCSE 考纲中只研究匀加速运动。若加速度不恒定，则需要用到微积分，这超出了本阶段的学习范围。

4. Displacement–Time Graphs | 位移—时间图像

A displacement–time graph (s–t graph) plots displacement s on the vertical axis and time t on the horizontal axis. The key interpretations are:

位移—时间图（s–t 图）以位移 s 为纵轴、时间 t 为横轴。关键解读如下：