📚 Maths Mechanics MS: Kinematics, Forces and Momentum Exam Skills | 数学力学MS：运动学、力与动量考点精讲
Mechanics questions in A-level Maths often look different from pure maths problems because they require a careful translation of physical situations into equations. This revision guide covers the core mechanics skills: vectors, SUVAT equations, Newton's laws, forces, friction, connected particles, momentum, and moments. Each section pairs an English explanation with a Chinese explanation so you can check your understanding from both sides.
A-level 数学中的力学题与纯数学题不同，因为需要将物理情景准确地转化为方程。本文覆盖力学核心技能：矢量、SUVAT 方程、牛顿定律、力、摩擦、连接体、动量和力矩。每一节都提供中英文对照，帮助你从两个角度检查理解。
1. Scalars and Vectors | 标量与矢量
In mechanics we first separate scalar and vector quantities. A scalar has magnitude only, while a vector has both magnitude and direction. Direction is essential when adding, subtracting, or resolving quantities.
在力学中我们首先区分标量和矢量。标量只有大小，而矢量既有大小又有方向。在加减或分解物理量时，方向至关重要。
Common scalars include distance, speed, mass, time, energy, and work. Common vectors include displacement, velocity, acceleration, force, momentum, and impulse.
常见标量包括距离、速率、质量、时间、能量和功。常见矢量包括位移、速度、加速度、力、动量和冲量。
When two vector quantities act at an angle, use a tip-to-tail diagram or component method. Never add magnitudes directly unless the vectors are parallel in the same direction.
当两个矢量成一定角度时，应使用三角形法则或分量法。除非两个矢量同向平行，否则不能直接相加大小。
- Scalars: distance, speed, time, mass, energy
- Vectors: displacement, velocity, acceleration, force, momentum
2. Displacement, Velocity and Acceleration | 位移、速度与加速度
Displacement s is the straight-line distance from the starting point to the final point in a stated direction. Distance is the total length of the path travelled, so distance can be greater than the magnitude of displacement.
位移 s 是从起点到终点的直线距离，并带有方向。距离是运动路径的总长度，因此距离可以大于位移的大小。
Velocity v is the rate of change of displacement, while speed is the rate of change of distance. Acceleration a is the rate of change of velocity, measured in m s⁻². Negative acceleration is often called deceleration or retardation.
速度 v 是位移对时间的变化率，而速率是距离对时间的变化率。加速度 a 是速度对时间的变化率，单位是 m s⁻²。负加速度常称为减速度或负加速度。
Average acceleration is given by:
平均加速度由下式给出：
a = (v − u) / t
ime taken. Unit conversion is a frequent skill: 1 km h⁻¹ = (1000/3600) m s⁻¹ = 5/18 m s⁻¹.
其中 u 是初速度，v 是末速度，t 是所用时间。单位换算也是常见考点：1 km h⁻¹ = (1000/3600) m s⁻¹ = 5/18 m s⁻¹。
3. The SUVAT Equations | SUVAT 方程
For constant acceleration a over time t, with initial velocity u, final velocity v, and displacement s, the five SUVAT equations apply only when acceleration is constant. If acceleration changes, you must use calculus or graph methods instead.
在加速度 a 恒定、时间为 t、初速度为 u、末速度为 v、位移为 s 的条件下，五个 SUVAT 方程适用。如果加速度变化，则必须改用微积分或图像方法。
| Equation | 方程 | Missing quantity | 不含量 | Typical use | 典型用法 |
| v = u + at | s | Find final velocity |
| s = ut + ½at² | v | Find displacement |
| v² = u² + 2as | t | Link velocities and distance |
| s = ½(u + v)t | a | Use average velocity |
| s = vt − ½at² | u | Use when final velocity is known |
Choose the equation by listing the known quantities and the quantity you need. Always assign a positive direction, especially when u and a may have opposite signs.
选择方程时先列出已知量和所求量。始终规定正方向，特别是当 u 和 a 符号相反时更要小心。
4. Motion Graphs and Area under a Curve | 运动图像与曲线下面积
A velocity-time graph is one of the most useful tools in mechanics. The gradient of the graph gives acceleration, the area under the graph gives displacement, and the y-intercept gives the initial velocity.
速度-时间图像是力学中最有用的工具之一。图像的斜率表示加速度，曲线下面积表示位移，纵轴截距表示初速度。
A displacement-time graph gives velocity as its gradient. A horizontal line on a displacement-time graph means the object is stationary. An acceleration-time graph gives change in velocity as the area under the curve.
位移-时间图像的斜率表示速度。位移-时间图像中的水平线表示物体静止。加速度-时间图像的面积表示速度变化量。
is one of the SUVAT equations. This confirms that graph methods and algebraic methods are equivalent.
对于直线速度-时间图像，面积为梯形，因此总位移 = ½(u + v)t，这正是 SUVAT 方程之一。这说明图像法与代数法是等价的。
5. Newton's Laws of Motion | 牛顿运动定律
Newton's first law states that an object remains at rest or moves with constant velocity unless acted on by a resultant external force. This means constant velocity does not require a forward force; it implies zero resultant force.
牛顿第一定律指出，物体在没有合外力作用时保持静止或匀速直线运动。这意味着匀速运动不需要向前的力；它说明合外力为零。
Newton' , where F is the resultant force in newtons, m is mass in kg, and a is acceleration in m s⁻². In vector form, the acceleration is in the same direction as the resultant
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