Physics Equations: Recall, Rearrangement and Application
GCSE Physics is the only science with a list of equations that must be recalled from memory, and roughly 30 percent of the marks on the papers are for maths skills. Around two dozen equations must be learned, including work done, kinetic energy, gravitational potential energy, power, efficiency, charge, density, wave speed and momentum, since not every equation is given on the physics equation sheet in the exam.
Before you start
No specific prerequisites - this is a good place to start.
Method
- List the quantities in the question with their symbols and units before doing anything: write down what you are given and what you are asked for, so the right equation becomes obvious.
- Convert every quantity to SI units first: metres, kilograms, seconds, joules, watts, amperes, volts. Convert kilojoules and kilowatts by multiplying by 1000, minutes and hours to seconds, and centimetres to metres by dividing by 100.
- Write the equation in symbols before substituting, because the first mark is for the equation and it is awarded even if the arithmetic later goes wrong.
- Rearrange before substituting, not after, and use the triangle relationship for any equation of the form a = b x c: cover the quantity you want to find.
- Substitute the numbers with their units, calculate, then state the answer with its unit and to a sensible number of significant figures, usually matching the least precise data in the question.
- Sense check the size of the answer: a car's kinetic energy in the hundreds of kilojoules is reasonable, a person's power output of 10 000 W is not. An answer out by exactly 1000 usually means a kilo prefix was missed.
Worked example
A 1200 kg car is travelling at 20 m/s. Calculate its kinetic energy, then find the average braking force needed to stop it in a distance of 40 m.
- Write the kinetic energy equation: kinetic energy = 0.5 x mass x speed squared.
- Substitute: 0.5 x 1200 x 20 squared = 0.5 x 1200 x 400.
- Calculate: 0.5 x 1200 = 600, and 600 x 400 = 240 000 J, which is 240 kJ.
- For the braking force, use the fact that the work done by the brakes equals the kinetic energy transferred: work done = force x distance.
- Rearrange for force: force = work done / distance = 240 000 / 40.
- Calculate: 240 000 / 40 = 6000 N. Final answers: kinetic energy 240 000 J, braking force 6000 N.
Practice questions
Try each question, then tap to reveal the answer.
Q1State the equation for work done.Show answer
Answer: Work done = force x distance moved along the line of action of the force, in joules.
Q2Convert 3.5 kJ into joules.Show answer
Answer: 3.5 x 1000 = 3500 J.
Q3Write the equation linking power, energy and time, and rearrange it for time.Show answer
Answer: Power = energy transferred / time, so time = energy transferred / power.
Q4Calculate the gravitational potential energy gained by a 60 kg person climbing 5 m. (g = 9.8 N/kg)Show answer
Answer: 60 x 9.8 x 5 = 2940 J.
Q5A device transfers 4500 J in 90 s. Calculate its power.Show answer
Answer: 4500 / 90 = 50 W.
Q6Give the equation for wave speed and its units.Show answer
Answer: Wave speed = frequency x wavelength, in metres per second, with frequency in hertz and wavelength in metres.
Q7Why should you write down the equation even if you cannot finish the calculation?Show answer
Answer: Marks are awarded in stages: one for the correct equation and one for correct substitution, both of which can be earned without reaching the right final answer.
Exam-style questions
Written in the style of a GCSE Science exam paper, with a full mark scheme.
A kettle transfers 180 kJ of energy in 2 minutes. Calculate its power output in watts.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A student writes: 'A 2 kW heater running for 30 minutes transfers 60 J.' Identify the error, and calculate the correct value.
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Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
See real GCSE Science past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the physics equations: recall, rearrangement and application worksheet pack - 15 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 10 of GCSE Physics Workbook, the whole course as one free printable PDF.
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