📚 AS Physics: Mastering Calculation Problems | AS 物理：计算题专项训练
Many AS Physics students find calculation questions the most challenging part of the exam. Success depends not just on knowing the formulae, but on a systematic approach to interpreting the problem, selecting the right equation, converting units and checking your answer. This masterclass walks you through the essential topics and skills, with paired English–Chinese explanations and worked examples to help you build confidence and accuracy.
许多 AS 物理学生觉得计算题是考试中最棘手的部分。要想拿到高分，不仅要熟记公式，还需要系统地训练审题、选择方程、单位换算和答案验证。这篇专项训练将带你梳理核心专题与技巧，每个要点都提供英中对照讲解和例题，帮助你建立信心、减少失误。
1. Extracting Information and Choosing the Right Formula | 提取信息与选择公式
Begin by reading the question twice. Underline or write down every numerical value together with its symbol and unit, and also note any qualitative clues such as ‘starts from rest’ (u = 0) or ‘comes to a stop’ (v = 0). This immediate translation into variables makes it much easier to see which SUVAT, energy or force equation is relevant.
先把题目读两遍。划出或抄下每一个数值及其物理符号和单位，同时留意像“由静止开始”(u = 0)或“停下”(v = 0)这样的文字线索。把文字转换成变量后，就很容易判断该用运动学方程、能量方程还是牛顿定律。
Once you have the list of knowns and unknowns, scan your formula sheet for an equation that connects exactly those quantities. If a required quantity is missing from your list, think about intermediate steps – often you need to find time, acceleration or a component of force first.
列出已知量和未知量之后，快速浏览公式表，找到能直接联系这些量的方程。如果缺少某个中间量，通常需要先求出时间、加速度或者某个力的分量。
A common trap is using a formula just because it looks familiar. Always check that every symbol in the equation is genuinely known or can be deduced. For instance, using v² = u² + 2as requires knowing the displacement s, so do not apply it if s is what you are trying to find alongside another unknown.
常见的陷阱是看到眼熟的公式就直接套用。一定要确认方程中每个物理量真正已知或可以推导。例如，v² = u² + 2as 必须已知位移 s，如果 s 正好也是要求的目标之一，就不能单独靠它求解。
2. Unit Conversions and Significant Figures | 单位换算与有效数字
Mixed units are one of the biggest sources of lost marks. Always convert to SI base units before substituting numbers: length in metres (m), mass in kilograms (kg), time in seconds (s). Remember that 1 cm² = 1 × 10⁻⁴ m², not 10⁻² m², and 1 km/h = (1000/3600) m/s ≈ 0.2778 m/s.
单位混乱是丢分最大的原因之一。代入数据前，一律转换成国际单位制：长度用米 (m)，质量用千克 (kg)，时间用秒 (s)。特别注意 1 cm² = 1 × 10⁻⁴ m²，而不是 10⁻² m²；1 km/h = (1000/3600) m/s ≈ 0.2778 m/s。
Give your final answer to the same number of significant figures as the least precise piece of data given in the question. Unless told otherwise, three significant figures is usually a safe choice. Avoid rounding intermediate results; keep them in your calculator and only round at the end.
最终答案的有效数字位数应与题目中给出数据中精度最低的一致。如果没有特别说明，通常保留三位有效数字。中间计算结果不要四舍五入，保存在计算器中，最后一步再取整。
When dealing with very large or very small numbers, use standard form (scientific notation) and the ×10ˣ key on your calculator. A common error is writing 0.0035 m as 3.5 × 10³ m; careful with the sign of the exponent.
遇到非常大或非常小的数字时，请使用科学记数法并按计算器上的 ×10ˣ 键。常见的失误是把 0.0035 m 写成 3.5 × 10³ m，一定要注意指数的正负号。
3. Kinematics: Using SUVAT Equations | 运动学：SUVAT 方程的应用
The five SUVAT equations link displacement s, initial velocity u, final velocity v, acceleration a and time t. You must know them by heart, but more importantly, you must be able to select the one that includes the three knowns and the unknown you want.
SUVAT equations: v = u + a t | s = ut + ½ a t² | s = ½ (u + v) t | v² = u² + 2 a s | s = v t – ½ a t²
五个运动学方程将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系在一起。必须牢牢记住它们，但更重要的是能迅速选出包含三个已知量和你要求的那一个未知量的方程。
v = u + a t | s = ut + ½ a t² | s = ½ (u + v) t | v² = u² + 2 a s | s = v t – ½ a t²
Example: A cyclist accelerates from rest at 2.5 m/s² for 8.0 s. Find the final velocity and the distance travelled. Known: u = 0, a = 2.5 m/s², t = 8.0 s. For v, use v = u + a t → v = 0 + (2.5)(8.0) = 20 m/s. For s, use s = u t + ½ a t² → s = 0 + ½ (2.5)(8.0)² = 80 m.
例题：一位自行车手从静止开始，以 2.5 m/s² 的加速度运动 8.0 s，求末速度和位移。已知 u = 0, a = 2.5 m/s², t = 8.0 s。求 v 用 v = u + a t → v = 20 m/s；求 s 用 s = u t + ½ a t² → s = 80 m。
Always check that the sign convention is consistent throughout. Choose a positive direction at the start, and assign ‘+’ and ‘–’ accordingly to displacement, velocity and acceleration.
始终确保正方向一致。一开始就指定正方向，并将位移、速度和加速度的符号统一起来。
4. Dynamics: Resolving Forces and Newton’s Second Law | 动力学：力的分解与牛顿第二定律
For any object that is accelerating, start with a clear free-body diagram. Draw all forces as arrows, label them (weight mg, normal reaction N, tension T, friction Fr), and then resolve vectors parallel and perpendicular to the acceleration.
处理加速运动的物体时，先画一幅清晰的受力分析图。用箭头标出所有力，并注明名称（重力 mg，支持力 N，张力 T，摩擦力 Fr），然后将力沿加速度方向及其垂直方向进行分解。
Apply Newton’s second law in the form Fnet = m a. For a block sliding down a smooth incline of angle θ, the net force along the slope is mg sin θ, giving a = g sin θ. If friction is present, remember Fnet = mg sin θ – Fr.
运用牛顿第二定律 Fnet = m a。对于沿光滑斜面下滑的物块，沿斜面方向的合力为 mg sin θ，因此加速度 a = g sin θ。如果存在摩擦力，则 Fnet = mg sin θ – Fr。
When several objects are connected by a light inextensible string, treat the whole system as one to find the acceleration, then examine a single object to find the tension. This avoids solving simultaneous equations unnecessarily.
当多个物体由轻质且不可伸长的绳子连接时，可以先将系统视作整体求出加速度，再单独分析某个物体求绳的张力。这样可以避免不必要的联立方程。
5. Work, Energy, and Power: Avoiding Common Pitfalls | 功、能与功率：避开常见陷阱
The work done by a constant force is W = F s cos θ, where θ is the angle between the force and the displacement. If the force is perpendicular to the motion (e.g. normal reaction, or centripetal force), it does no work.
恒力做功的计算公式为 W = F s cos θ，其中 θ 是力与位移之间的夹角。当力与运动方向垂直时（例如支持力或向心力），做功为零。
Kinetic energy Ek = ½ m v² and gravitational potential energy Ep = m g h can only be traded in the absence of non-conservative forces. If friction or air resistance acts, the work done against these forces equals the loss of mechanical energy.
动能 Ek = ½ m v² 和重力势能 Ep = m g h 只有在没有非保守力时才完全相互转化。如果有摩擦力或空气阻力，克服这些力所做的功等于机械能的减少量。
Power is the rate of doing work, P = W / t. For a constant force moving an object at steady speed v, power can also be written as P = F v. Make sure you use consistent units (watt = J/s).
功率是做功的快慢，P = W / t。若一个恒力使物体以恒定速度 v 运动，功率还可以写作 P = F v。务必保持单位一致（瓦特 = 焦耳/秒）。
6. Momentum and Impulse in Collisions | 碰撞中的动量与冲量
Momentum p = m v is a vector quantity, so direction matters. In one-dimensional problems, assign a positive direction and use ‘+’ and ‘–’ signs for velocities. The principle of conservation of momentum states that total momentum before an interaction equals total momentum afterwards, provided no external resultant force acts.
动量 p = m v 是矢量，因此方向非常重要。在一维问题中，先规定正方向，再用正负号表示速度。动量守恒定律指出，只要合外力为零，系统作用前的总动量等于作用后的总动量。
Impulse = change in momentum = F Δt. This is particularly useful when a force acts for a very short time, such as a kick or a collision. The area under a force–time graph also gives the impulse.
冲量等于动量的变化量，即 F Δt。当作用力时间很短时（如脚踢球或碰撞），这一关系尤为有用。力–时间图下方的面积也代表冲量。
For perfectly inelastic collisions, the objects stick together and move with a common velocity. In an explosion or firing problem, the initial momentum is usually zero, so the pieces must have equal and opposite momenta afterwards.
在完全非弹性碰撞中，物体粘在一起并以共同速度运动。在爆炸或发射问题中，初始动量通常为零，因此碎片必定获得大小相等、方向相反的动量。
7. Electricity: Series, Parallel and Internal Resistance | 电学：串联、并联与内阻
Ohm’s law V = I R and the power equations P = I V = I² R = V²/R are the foundation. When combining resistors, remember: series → Rtotal = R₁ + R₂ + …, same current; parallel → 1/Rtotal = 1/R₁ + 1/R₂ + …, same voltage across each branch.
欧姆定律 V = I R 以及功率公式 P = I V = I² R = V²/R 是基础。组合电阻时牢记：串联时 R总 = R₁ + R₂ + …，电流相同；并联时 1/R总 = 1/R₁ + 1/R₂ + …，各支路两端电压相同。
A real cell has internal resistance r. The terminal p.d. is V = ε – I r, where ε is the e.m.f. When a circuit is open, V ≈ ε; when it supplies a large current, the lost volts I r reduce the available voltage.
真实电池具有内阻 r。其端电压为 V = ε – I r，其中 ε 为电动势。电路开路时 V ≈ ε；当电路输出大电流时，损失的电压 I r 会降低路端电压。
Potential divider circuits allow you to obtain a fraction of the total voltage. The output voltage Vout = (R₂/(R₁+R₂)) × Vin. Pay close attention to whether a component is in series or parallel with the rest of the circuit.
分压电路可以获取总电压的一部分，输出电压 Vout = (R₂/(R₁+R₂)) × Vin。要特别留意元件与电路其余部分的连接方式是串联还是并联。
8. Waves: Calculating Frequency, Wavelength and Speed | 波动：频率、波长与波速的计算
The wave equation v = f λ is used across sound, water, light and mechanical waves on strings. Make sure you can rearrange it confidently to find any of the three quantities. Frequency f is measured in hertz (Hz), wavelength λ in metres (m).
波速方程 v = f λ 适用于声波、水波、光波以及弦上的机械波。你需要能熟练地变形求解任意一个量。频率 f 的单位是赫兹 (Hz)，波长 λ 的单位是米 (m)。
Refractive index n is defined as n = c / v (where c is the speed of light in vacuum) and also follows Snell’s law: n₁ sin θ₁ = n₂ sin θ₂. For a ray entering a denser medium, it bends towards the normal; the frequency remains unchanged but the wavelength shortens.
折射率 n 定义为 n = c / v（c 为真空中光速），同时遵循斯涅耳定律：n₁ sin θ₁ = n₂ sin θ₂。光线进入光密介质时向法线偏折；频率不变，但波长变短。
For standing waves on a string fixed at both ends, the fundamental wavelength λ = 2L. Harmonics follow as λn = 2L/n. The speed of the wave depends on tension T and linear density μ: v = √(T/μ).
对于两端固定的弦上的驻波，基频波长为 λ = 2L。泛频波长为 λn = 2L/n。波速取决于张力 T 和线密度 μ：v = √(T/μ)。
9. Materials: Stress, Strain and the Young Modulus | 材料：应力、应变与杨氏模量
Stress σ = F / A (unit: Pascal, Pa) and strain ε = ΔL / L₀ (no unit). The Young modulus E = σ / ε describes the stiffness of a material. For a given material, E is constant within the linear elastic region, and the stress–strain graph is a straight line obeying Hooke’s law.
应力 σ = F / A（单位：帕斯卡 Pa），应变 ε = ΔL / L₀（无单位）。杨氏模量 E = σ / ε 描述材料的刚性。对于给定材料，在弹性限度内 E 为定值，应力–应变图为一条符合胡克定律的直线。
When calculating extension, be careful to
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