IGCSE Edexcel Maths: Kinematics Key Points | IGCSE Edexcel 数学：运动学 考点精讲

📚 IGCSE Edexcel Maths: Kinematics Key Points | IGCSE Edexcel 数学：运动学 考点精讲

Kinematics is the study of motion without considering the forces that cause it. In IGCSE Edexcel Maths, you need to understand how to describe motion using quantities like displacement, velocity, and acceleration, interpret motion graphs, and apply the equations of uniform acceleration (SUVAT). Mastery of these concepts is essential for solving problems on straight-line motion and for building a solid foundation in mechanics.

运动学是研究运动而不考虑引起运动的力的学科。在 IGCSE Edexcel 数学中，你需要掌握如何用位移、速度和加速度等物理量描述运动，解读运动图像，并应用匀加速运动方程（SUVAT）。熟练掌握这些概念对于解决直线运动问题和为力学打下坚实基础至关重要。

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1. Displacement, Velocity and Acceleration | 位移、速度和加速度

Displacement (s) is the distance travelled in a given direction; its unit is the metre (m). Velocity (v) is the rate of change of displacement, and acceleration (a) is the rate of change of velocity.

位移 (s) 是在给定方向上移动的距离；单位是米 (m)。速度 (v) 是位移的变化率，加速度 (a) 是速度的变化率。

Average velocity = total displacement / total time

平均速度 = 总位移 / 总时间

Acceleration a = (v – u) / t

加速度 a = (v – u) / t

Here u is the initial velocity, v is the final velocity, and t is the time taken for the change. These quantities are vectors, so direction matters.

其中 u 是初速度，v 是末速度，t 是变化所用的时间。这些量都是矢量，因此方向很重要。

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2. Scalar and Vector Quantities | 标量与矢量

Distance is a scalar – it only tells you how much ground an object has covered, with no direction. Displacement is a vector – it tells you how far and in which direction the object is from its starting point.

距离是标量——它只告诉你物体移动了多少路程，没有方向。位移是矢量——它告诉你物体距离起点有多远以及方向如何。

Speed = distance / time is scalar; velocity = displacement / time is vector. When solving problems, always choose a positive direction (e.g., rightwards or upwards) and treat motion in the opposite direction as negative.

速率 = 路程 / 时间是标量；速度 = 位移 / 时间是矢量。解题时，一定要选择一个正方向（如向右或向上），并将相反方向的运动视为负值。

Likewise, acceleration can be positive (speeding up in the positive direction) or negative (slowing down, or speeding up in the negative direction). Using signs consistently avoids mistakes in SUVAT calculations.

同样，加速度可以是正的（在正方向上加速）或负的（减速，或在负方向上加速）。始终使用符号可以避免 SUVAT 计算中的错误。

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3. Displacement-Time Graphs (s-t Graphs) | 位移-时间图

On an s-t graph, time is plotted on the horizontal axis and displacement on the vertical axis. A straight line indicates constant velocity, and the gradient of that line equals the velocity.

在位移-时间图中，时间标在横轴，位移标在纵轴。直线表示匀速运动，直线的斜率等于速度。

If the graph is curved, the velocity is changing. The instantaneous velocity at any point is given by the gradient of the tangent to the curve at that point.

如果图像是曲线，则速度在变化。任一点的瞬时速度由该点切线的斜率给出。

A horizontal line on an s-t graph means the object is stationary (displacement is not changing). The steeper the line, the greater the speed.

s-t 图中的水平线表示物体静止（位移不变）。线越陡，速率越大。

Average velocity over a time interval = (change in displacement) / (change in time) = slope of the chord joining the two points.

某段时间内的平均速度 = 位移变化量 / 时间变化量 = 连接两点的弦的斜率。

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4. Velocity-Time Graphs (v-t Graphs) | 速度-时间图

A v-t graph shows velocity on the y-axis and time on the x-axis. The gradient of the graph gives the acceleration. A straight, sloping line means constant acceleration; a horizontal line means zero acceleration (constant velocity).

速度-时间图以 y 轴表示速度，x 轴表示时间。图像的斜率表示加速度。倾斜的直线表示匀加速；水平线表示加速度为零（匀速）。

Acceleration = gradient of v-t graph

加速度 = v-t 图的斜率

The area under a v-t graph between two times represents the displacement (change in position) during that interval. If the graph dips below the time axis, the area counts as negative, indicating motion in the negative direction.

v-t 图中，两时刻之间的面积代表该时间段内的位移。如果图像低于时间轴，该面积计为负，表示向负方向运动。

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5. Finding Acceleration from a v-t Graph | 从 v-t 图求加速度

To find acceleration between two points on a v-t graph, calculate the gradient: a = (v2 – v1) / (t2 – t1). If the line slopes upwards, acceleration is positive; if it slopes downwards, acceleration is negative (often called deceleration).

要计算 v-t 图上两点间的加速度，就求斜率：a = (v2 – v1) / (t2 – t1)。如果线向上倾斜，加速度为正；如果

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