📚 GCSE Physics: Calculation Practice | GCSE 物理：计算题专项训练
GCSE Physics calculations appear in nearly every topic, and mastering them is key to achieving a top grade. This guide focuses on the most common formula‑based problems, offering step‑by‑step advice on identifying quantities, converting units, rearranging equations, and presenting your working clearly. Practising these examples will build your confidence for the exam.
GCSE 物理的计算题几乎出现在每个专题中，掌握它们是获得高分的关键。本指南聚焦最常见的公式类题目，逐步讲解如何确定物理量、转换单位、变形公式以及清晰展示解题过程。通过练习这些例题，你将建立考试信心。
| Formula | 中文名称 |
|---|---|
| v = d ÷ t | 速度公式 |
| a = (v − u) ÷ t | 加速度公式 |
| F = m × a | 牛顿第二定律 |
| W = F × d | 做功 |
| GPE = m × g × h | 重力势能 |
| KE = ½; × m × v² | 动能 |
| P = W ÷ t (or E ÷ t) | 功率 |
| η = (useful output ÷ total input) × 100% | 效率 |
| ρ = m ÷ V | 密度 |
| p = F ÷ A | 压强 |
| V = I × R | 欧姆定律 |
| P = I × V, P = I²R | 电功率 |
| E = P × t | 电能 |
| ΔE = m × c × Δθ | 比热容 |
| E = m × L | 比潜热 |
| v = f × λ | 波速公式 |
1. Speed, Distance & Time | 速度、距离和时间
Use v = d ÷ t where v is speed, d is distance and t is time. The standard SI unit for speed is metres per second (m/s). If a distance is given in kilometres and time in hours, the speed will be in km/h. You can convert between m/s and km/h using the factor 3.6: to change m/s to km/h, multiply by 3.6; to change km/h to m/s, divide by 3.6. Always show the substitution step and write the correct unit.
使用 v = d ÷ t，其中 v 表示速度，d 表示距离，t 表示时间。速度的标准国际单位是米每秒（m/s）。如果距离用千米、时间用小时，则速度单位为 km/h。m/s 与 km/h 可通过系数 3.6 换算：从 m/s 换算为 km/h 需乘以 3.6；从 km/h 换算为 m/s 则除以 3.6。务必写出代入步骤并标明正确单位。
Example: A car travels at a constant speed of 90 km/h. How far does it travel in 2 hours?
例题：一辆汽车以 90 km/h 的恒定速度行驶，2 小时内行驶多远？
= v × t = 90 × 2 = 180 km. If you need the answer in metres, convert: 180 km = 180 000 m.
解答：d = v × t = 90 × 2 = 180 km。如需以米为单位，可换算：180 km = 180 000 m。
2. Acceleration | 加速度
Acceleration is the rate of change of velocity. The equation is a = (v − u) ÷ t sup2;). Deceleration is simply negative acceleration. When an object accelerates from rest, u = 0.
加速度是速度的变化率。公式为 a = (v − u) ÷ t，其中 a 为加速度，v 为末速度，u 为初速度，t 为所用时间。加速度的单位是米每二次方秒（m/s²）。减速即为负加速度。物体由静止开始加速时，u = 0。
Example: A sprinter increases her velocity from 0 m/s to 8 m/s in 2 seconds. Calculate her acceleration.
例题：一位短跑运动员在 2 秒内从 0 m/s 加速到 8 m/s。计算她的加速度。
Solution: a = (8 − 0) ÷ 2 = 4 m/s²;.
解答：a = (8 − 0) ÷ 2 = 4 m/s²;。
3. Newton's Second Law | 牛顿第二定律
The relationship between force, mass and acceleration is given by F = m × a is given in grams, divide by 1000. This formula is often combined with other equations such as W = mg.
力、质量与加速度的关系由 F = m × a 给出，其中 F 为合外力，单位牛顿（N）；m 为质量，单位千克（kg）；a 为加速度，单位 m/s²。务必确认质量单位为 kg；若题目以克为单位，需除以 1000。该公式常与 W = mg 等公式结合使用。
Example: A resultant force of 600 N acts on a car of mass 1200 kg. What is its acceleration?
例题：一辆质量为 1200 kg 的汽车受到 600 N 的合外力作用。它的加速度是多少？
Solution: a = F ÷ m = 600 ÷ 1200 = 0.5 m/s²;.
解答：a = F ÷ m = 600 ÷ 1200 = 0.5 m/s²;。
4. Work Done & Energy Transfer | 做功与能量转移
When a force moves an object, work is done on the object. W = F × d, where W is work done in joules (J), F is the force in newtons (N) and d is the distance moved in the direction of the force in metres (m). Work done is equal to the amount of energy transferred. If the force is perpendicular to the displacement, no work is done.
当力使物体移动时，便做了功。W = F × d，其中 W 为做功，单位焦耳（J）；F 为力，单位牛顿（N）；d 为在力的方向上移动的距离，单位米（m）。做功等于转移的能量。若力与位移方向垂直，则不做功。
Example: A person lifts a box with a force of 50 N through a vertical distance of 1.5 m. Calculate the work done.
例题：一个人用 50 N 的力将一个箱子竖直提起 1.5 m，计算所做的功。
Solution: W = 50 × 1.5 = 75 J.
解答：W = 50 × 1.5 = 75 J。
5. Gravitational Potential Energy & Kinetic Energy | 重力势能与动能
Gravitational potential energy (GPE) depends on mass, height and gravitational field strength: GPE = m × g × h. On Earth, g is usually 9.8 N/kg, but 10 N/kg is often used in exams. Kinetic energy (KE) depends on mass and speed: KE = ½; × m × v². When friction is negligible, the loss in GPE equals the gain in KE.
重力势能取决于质量、高度和引力场强：GPE = m × g × h。地球上 g 通常取 9.8 N/kg，考试中常用 10 N/kg。动能取决于质量和速度：KE = ½; × m × v²。当摩擦力可忽略时，重力势能的减少量等于动能的增加量。
a height of 8 m. Take g = 10 N/kg. Find its kinetic energy just before hitting the ground.
例题：一个 0.5 kg 的小球从 8 m 高处落下，取 g = 10 N/kg。求它落地前一瞬间的动能。
on: Loss of GPE = mgh = 0.5 × 10 × 8 = 40 J. Assuming no air resistance, KE gained = 40 J.
解答：减少的重力势能 = mgh = 0.5 × 10 × 8 = 40 J。假设无空气阻力，获得的动能 = 40 J。
6. Power & Efficiency | 功率与效率
Power is the rate of doing work or transferring energy: P = W ÷ t (or P = E ÷ t). The SI unit is the watt (W), where 1 W = 1 J/s. Efficiency is a measure of how much useful energy or power is output compared with the total input: η = (useful output ÷ total input) × 100%. It can be expressed as a decimal or a percentage; no machine can be more than 100% efficient.
功率是做功或转移能量的速率：P = W ÷ t（或 P = E ÷ t）。国际单位为瓦特（W），1 W = 1 J/s。效率衡量有用能量或功率的输出占总输入的比值：η = (有用输出 ÷ 总输入) × 100%。效率可用小数或百分数表示；任何机器的效率都不可能超过 100%。
Example: A motor does 1200 J of useful work in 60 s. The total electrical energy supplied is 2000 J. Calculate its power output and efficiency.
例题：一台电动机在 60 s 内做有用功 1200 J，总输入电能为 2000 J。计算其输出功率和效率。
Solution: Power output = 1200 ÷ 60 = 20 W. Efficiency = (1200 ÷ 2000) × 100% = 60%.
解答：输出功率 = 1200 ÷ 60 = 20 W。效率 = (1200 ÷ 2000) × 100% = 60%。
7. Density & Pressure | 密度与压强
Density mass per unit volume: ρ = m ÷ V dard unit is kg/m³, but you may also see g/cm³ (1 g/cm³ = 1000 kg/m³). Pressure is force per unit area: p = F ÷ A ls (Pa), where 1 Pa = 1 N/m²;. In fluid pressure problems, p = hρg is also common.
密度是单位体积的质量：ρ = m ÷ V，其中 ρ 为密度，m 为质量，V 为体积。国际单位为 kg/m³，也常用 g/cm³（1 g/cm³ = 1000 kg/m³;）。压强是单位面积上的压力：p = F ÷ A。压强单位为帕斯卡（Pa），1 Pa = 1 N/m²;。流体压强问题中，p = hρg 也很常见。
Example: A wooden block of mass 0.6 kg has a volume of 0.0008 m³. Calculate its density.
例题：一块木头的质量为 0.6 kg，体积为 0.0008 m³。计算其密度。
Solution: ρ = m ÷ V = 0.6 ÷ 0.0008 = 750 kg/m³;.
解答：ρ = m ÷ V = 0.6 ÷ 0.0008 = 750 kg/m³;。
8. Ohm's Law & Resistance | 欧姆定律与电阻
V = I × R n be rearranged as I = V ÷ R and R = V ÷ I. In series circuits, the total resistance is the sum of individual resistances. Check whether the question involves a fixed resistor or a variable component such as a filament lamp.
V = I × R 描述了电压、电流和电阻的关系。V 单位为伏特（V），I 为安培（A），R 为欧姆（Ω）。公式可变形为 I = V ÷ R 和 R = V ÷ I。在串联电路中，总电阻等于各电阻之和。注意题目中是用定值电阻还是灯丝等变化元件。
Example: A resistor of 15 Ω is connected to a 6 V battery. What current flows through it?
例题：一个 15 Ω 的电阻接在 6 V 电池上。通过它的电流是多少？
Solution: I = V ÷ R = 6 ÷ 15 = 0.4 A.
解答：I = V ÷ R = 6 ÷ 15 = 0.4 A。
9. Electrical Power & Energy | 电功率与电能
Two common forms for electrical power are P = I × V and P = I²; × R. Power is measured in watts (W). The energy transferred by an electrical device is E = P × t ds to give energy in joules. In domestic electricity, energy is often measured in kilowatt‑ kW·h = 3 600 000 J. Remember to convert time to seconds unless you are dealing with kW·h.
电功率的常用形式是 P = I × V 和 P = I²; × R。功率单位为瓦特（W）。用电器消耗的电能由 E = P × t 计算，t 以秒为单位时，能量单位为焦耳。生活用电常用千瓦时（kW·h）：1 kW·h = 3 600 000 J。除非使用 kW·h，否则时间通常要转换为秒。
Example: A heater runs on 230 V and draws a current of 4 A. Calculate its power and the energy consumed in 10 minutes.
例题：一个电暖器在 230 V 下工作，电流为 4 A。计算其功率及 10 分钟内消耗的电能。
= 4 × 230 = 920 W. t = 10 × 60 = 600 s, so E = P × t = 920 × 600 = 552 000 J (or 552 kJ).
解答：P = I × V = 4 × 230 = 920 W。t = 10 × 60 = 600 s，则 E = P × t = 920 × 600 = 552 000 J（即 552 kJ）。
10. Specific Heat Capacity | 比热容
The amount of thermal energy needed to change an object's temperature is given by ΔE = m × c × Δθ. Here ΔE is the thermal energy in joules, m is mass in kg, c is the specific heat capacity in J/(kg·°C) and Δθ is the temperature change in °C. Water has a high specific heat capacity (4200 J/(kg·°C)). Always use the temperature difference, not the final temperature alone.
改变物体温度所需的热量由 ΔE = m × c × Δθ 给出。ΔE 为热能量，单位焦耳；m 为质量，单位 kg；c 为比热容，单位 J/(kg·°C)；Δθ 为温度变化，单位 °C。水的比热容很大（4200 J/(kg·°C)）。解题时必须使用温度变化量，而不是只用末温。
Example: How much energy is needed to heat 2 kg of water from 20°C to 100°C? (c = 4200
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