📚 AQA AS Mathematics Unit 4 Mechanics 1 June 2019 | AQA AS 数学第四单元力学1 2019年6月卷
This revision article reviews the main skills and models examined in the AQA AS Mathematics Unit 4 paper for Mechanics 1, using the June 2019 paper as a reference point. It brings together the core formulas, standard problem types and examiner tips to help you build confidence before the exam.
本文以 2019 年 6 月 AQA AS 数学第四单元力学 1 试卷为参照，复习主要技能和力学模型，汇总核心公式、常见题型和考官建议，帮助你在考前建立信心。
1. Exam Overview and Paper Structure | 考试概览与试卷结构
The Unit 4 Mechanics 1 paper typically contains a mix of short calculation questions and longer structured problems set in realistic physical situations. You should expect to model objects as particles, use constant-acceleration kinematics, apply Newton's laws, and work with force diagrams.
第四单元力学 1 试卷通常包含短计算题和较长的结构性问题，题目设置在真实物理情境中。你需要把物体模型化为质点，使用匀加速运动学公式，应用牛顿定律，并处理受力图。
- Core topics: SUVAT equations, velocity-time graphs, Newton's second law, connected particles, friction, momentum, vectors and moments.
- 核心考点：匀加速运动公式、速度-时间图像、牛顿第二定律、连接体、摩擦力、动量、向量和力矩。
- Marks are awarded for clear diagrams, correct resolution of forces and accurate units.
- 清晰的受力图、正确的力的分解和准确的单位都会影响得分。
2. Essential SUVAT Toolkit | 核心匀加速运动公式
You must be able to choose the correct constant-acceleration formula from the SUVAT set. The four standard equations are shown below. In each one, s is displacement, u is initial velocity, v is final velocity, a is acceleration and t is time.
你必须能够从匀加速运动公式中正确选择公式。下面是四个标准方程，其中 s 表示位移，u 表示初速度，v 表示末速度，a 表示加速度，t 表示时间。
| v = u + at | v = u + at |
| s = ut + ½at² | s = ut + ½at² |
| v² = u² + 2as | v² = u² + 2as |
| s = ½(u + v)t | s = ½(u + v)t |
Always write down the values you know and the variable you are trying to find. Then pick the equation that includes only those symbols.
始终先写下已知量和待求量，然后选择只包含这些符号的公式。
v² = u² + 2as
ws down with displacement known, the equation v² = u² + 2as avoids solving for time first.
例如，当汽车减速且已知位移时，使用 v² = u² + 2as 可以避免先求时间。
3. Velocity-Time Graph Skills | 速度-时间图像技巧
A velocity-time graph gives acceleration as the gradient and displacement as the area under the graph. Many Unit 4 questions ask you to sketch or read these graphs for motion that includes constant acceleration and constant velocity.
速度-时间图像中，加速度等于斜率，位移等于图像下方的面积。第四单元的许多题目要求你绘制或读取包含匀加速和匀速阶段的运动图像。
- Gradient of a velocity-time graph = acceleration.
- 速度-时间图像的斜率 = 加速度。
- Area under a velocity-time graph = displacement.
- 速度-时间图像下的面积 = 位移。
- A horizontal line means constant velocity, so acceleration is zero.
- 水平线表示速度不变，因此加速度为零。
When the graph is made of straight line segments, split the area into rectangles and triangles. Remember that area below the time axis represents displacement in the negative direction.
当图像由直线段组成时，可把面积分成矩形和三角形。记住，时间轴下方的面积表示反方向的位移。
4. Resolving Forces and Newton's Second Law | 力的分解与牛顿第二定律
Newton' it in one direction at a time, usually along the plane of motion or along the line of the tension.
牛顿第二定律指出，作用在质点上的合力等于质量乘以加速度：F = ma。你必须一次沿一个方向应用它，通常沿运动方向或张力方向。
F = ma
When forces act at an angle, resolve them into perpendicular components. For a force F at angle θ to the horizontal, the horizontal component is F cos θ and the vertical component is F sin θ.
当力的方向与运动方向成一定角度时，需要将力分解为互相垂直的分量。若力 F 与水平方向成 θ 角，则水平分量为 F cos θ，竖直分量为 F sin θ。
- Draw a clear force diagram before resolving.
- 分解前先画出清晰的受力图。
- Take the direction of acceleration as positive when writing F = ma.
- 写 F = ma 时，通常取加速度方向为正方向。
5. Connected Particles and Pulleys | 连接体与滑轮
Connected particle problems often involve two objects linked by a light, inextensible string passing over a smooth pulley. The string has the same tension throughout, and the particles have the same magnitude of acceleration.
连接体问题通常涉及两个物体通过一根轻质不可伸长的绳子绕过光滑滑轮相连。绳子各处的张力相同，两个物体的加速度大小也相同。
To solve these problems, write an equation of motion for each particle separately. Then solve the simultaneous equations for acceleration and tension.
解题时需要分别对每个质点列出运动方程，然后联立求解加速度和张力。
For mass m₁: m₁g - T = m₁a
For mass m₂: T - m₂g = m₂a
Adding these equations often eliminates the tension T and gives the acceleration directly, after which T can be found by substitution.
将两个方程相加通常可以消去张力 T，直接求出加速度，然后再代入求出 T。
6. Friction and Limiting Equilibrium | 摩擦力与极限平衡
ficient of friction. At the point of slipping, friction reaches its limiting value F = μR.
摩擦力阻碍滑动的发生。摩擦力满足 F ≤ μR，其中 R 是法向反作用力，μ 是摩擦系数。当物体即将滑动时，摩擦力达到极限值 F = μR。
F ≤ μR
d plane, resolve the weight into components parallel and perpendicular to the plane first.
对于水平面上的质点，法向反作用力通常等于其重力，即 R = mg。在斜面上，需先把重力分解为沿斜面和垂直于斜面的两个分量。
- Use limiting friction only when the object is on the point of moving.
- 只有当物体即将移动时才使用极限摩擦力。
- Common exam question: find the least force required to overcome friction or the maximum slope angle before slipping.
- 常见考题：求克服摩擦所需的最小力，或物体开始滑动前的最大斜面角度。
7. Momentum and Impulse | 动量与冲量
lse is the change in momentum caused by a force acting over time. Impulse can be written as Ft or as a vector change m(v - u).
动量定义为 p = mv，冲量是力在一段时间内作用引起的动量变化。冲量可以写成 Ft，也可以写成向量形式的动量变化 m(v - u)。
Impulse = Ft = mv - mu
In Unit 4, momentum questions often involve collisions or a particle moving in a straight line. Always choose a positive direction and keep vector signs consistent.
第四单元的动量题通常涉及碰撞或沿直线运动的质点。做题时一定要选定正方向，并保持向量符号一致。
If two particles collide, the total momentum before the collision equals the total momentum after the collision, provided no external resultant force acts.
如果两个质点发生碰撞，在没有外力合力的条件下，碰撞前的总动量等于碰撞后的总动量。
8. Vectors in Mechanics | 力学中的向量
In mechanics, displacement, velocity, acceleration and force are vector quantities. Unit 4 questions often use i and j unit vectors to represent horizontal and vertical components.
在力学中，位移、速度、加速度和力都是向量。第四单元的题目通常使用 i 和 j 单位向量表示水平和竖直分量。
r = 3i - 4j, v = 2i + 5jPublished by TutorHao | AS Mathematics Revision Series | aleveler.com
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