IGCSE Physics Formulas: Motion, Forces, Energy (CIE 0625)

Most candidates fail not because they cannot rearrange a formula, but because they reach for the wrong one. Cambridge IGCSE Physics (0625) gives you a formula sheet on Paper 4 (Extended) and on Paper 3 (Core), yet the names of quantities and the units catch people out under timed conditions. This guide groups the formulas the way examiners actually test them: motion first, then forces, then energy. Treat it as your shortcut to spotting which equation a question is asking for in under ten seconds.

Speed, velocity, acceleration

Speed is a scalar, velocity is a vector. The distinction matters in Paper 4 long-response questions where examiners want both magnitude and direction. The core relations are:

• average speed = total distance / total time, written v = s/t - acceleration = change in velocity / time taken, written a = (v - u) / t

For uniform acceleration there is one more relation that the syllabus expects you to use even though it is not always printed on the sheet:

• v^2 = u^2 + 2as

That third relation lets you solve any kinematics problem without time. Pick it whenever a question gives you initial velocity, final velocity and distance (or asks for one of those three).

Reading the graphs is half the marks

A surprising amount of motion marks come from graph interpretation, not algebra:

• on a distance vs time graph, the gradient is speed - on a speed vs time graph, the gradient is acceleration and the area under the line is the distance travelled

Examiners love asking you to find total distance from a triangular or trapezoidal speed against time graph. Always compute the area in two pieces (rectangle plus triangle) rather than as a single composite shape: you will lose fewer method marks if your arithmetic slips. For sustained drill on this topic, work through the [forces and motion complete guide](/igcse-physics-forces-motion-complete-guide) before moving on.

Every forces question in IGCSE Physics ultimately leans on F = ma. Memorise its three forms:

• F = ma when you want the resultant force on a moving object - a = F/m to find acceleration from a known force - m = F/a if you are asked for the mass (rare but it appears)

The trap: F here is the resultant (net) force. If a 2 kg trolley is pushed forward with 8 N while friction opposes it with 2 N, the resultant is 6 N and a = 3 m/s^2, not 4. Students who plug the applied force straight in lose two marks every time.

Weight, gravity and the value of g

• W = mg

Cambridge tells you to use g = 9.8 N/kg (or m/s^2) unless the question specifies otherwise. Some legacy past papers use 10 for cleaner arithmetic: read the stem. Weight is a force, measured in newtons, never in kilograms. Examiners deliberately give masses in grams to test unit awareness: convert to kilograms before substituting.

Moments, pressure, density and springs

These four show up in nearly every Paper 4 and most Paper 6 (practical):

• moment of a force = force x perpendicular distance from pivot (N m) - pressure p = F / A (Pa, with A in square metres) - density rho = m / V (kg/m^3 or g/cm^3) - Hooke's law F = k x (the spring constant k has units N/m or N/cm)

For pressure in fluids the syllabus adds:

• p = rho g h

This one trips students up because rho must be the density of the fluid, h is the depth below the surface, and the final answer often needs converting from pascals to kilopascals.

Kinetic energy:

• KE = (1/2) m v^2

Gravitational potential energy near the Earth's surface:

• GPE = m g h (the change in height, not absolute height)

Work done by a constant force:

• W = F d (where d is the distance moved in the direction of the force)

Power:

• P = E / t, or equivalently P = W / t

Conservation of energy is the most powerful idea in the whole 0625 syllabus: in a closed system, total energy is constant, so any kinetic energy lost becomes potential energy, thermal energy or sound energy. When a question says 'neglect air resistance' or 'assume the ramp is frictionless', it is inviting you to equate KE and GPE.

Efficiency

• efficiency = useful energy output / total energy input

The result is between 0 and 1 (or expressed as a percentage). If your answer is above 1 you have flipped the fraction. The same formula appears with power: efficiency = useful power output / total power input.

Units that examiners weaponise

Work and energy are both in joules (J). Power is in watts (W), where 1 W = 1 J/s. Distance must be in metres for these formulas, not centimetres. Time must be in seconds, not minutes. If you keep distances in cm or times in minutes, you will get a numerical answer that is off by a factor of 100 or 60, and the marker has no way to award method marks for an answer that disagrees with the mark scheme by a large factor.

Question:

a 0.5 kg ball is released from rest at the top of a 1.2 m smooth ramp. Calculate the speed of the ball at the bottom. (Take g = 9.8 N/kg.)

Step 1: identify the physics.

The ramp is smooth, so no work is done against friction. All the GPE converts to KE.

Step 2: write the energy equation.

• m g h = (1/2) m v^2

Step 3: cancel the mass (it appears on both sides) and solve for v.

• v^2 = 2 g h - v^2 = 2 x 9.8 x 1.2 = 23.52 - v = 4.85 m/s

Step 4: sanity check using kinematics.

Acceleration down a smooth ramp of height h and length L is a = g sin(theta) = g h / L. If the ramp is 1.5 m long, a = 9.8 x 1.2 / 1.5 = 7.84 m/s^2. Using v^2 = u^2 + 2 a L with u = 0 gives v^2 = 2 x 7.84 x 1.5 = 23.52, so v = 4.85 m/s. The two methods agree, which is the marker you should always look for in Paper 4 multi-step questions.

Marks the examiner is checking:

• correct identification of energy conservation (1 mark) - correct substitution with consistent units (1 mark) - correct rearrangement to v (1 mark) - final answer to 2 or 3 significant figures, with unit m/s (1 mark)

Notice that dropping the unit, or quoting 4.8513... m/s to five digits, loses the final accuracy mark even when the working is right. The mark scheme on real CIE 0625 papers is strict about significant figures. For the full anatomy of how marks are split on this style of question, see [the calculations students get wrong](/igcse-physics-calculations-students-get-wrong).

Paper 4 (Extended Theory, 1 hour 15 minutes) treats formulas as building blocks for multi-part questions. A typical 8 mark item might ask you to:

• calculate weight, then resultant force, then acceleration, then speed after a time - combine W = F d with P = W / t to find a motor's power - equate GPE and KE to find a landing speed, then use F = ma to find an impact force given a stopping distance

Paper 6 (Alternative to Practical) tests the same formulas but inside a graph or a table. You will be asked to plot points, draw a best fit line, find a gradient and identify what that gradient physically represents (often k from F = k x, or g from a pendulum experiment).

The most common slip across both papers is unit conversion. Time in minutes instead of seconds, mass in grams instead of kilograms, area in cm^2 instead of m^2. Build the habit of writing units beside every substitution and you will rescue 4 to 6 marks across the paper that other candidates throw away.

A tactical tip on multi-mark questions

In Paper 4 questions worth 5 or more marks, the examiner often tests three formulas in sequence. The first calculation feeds the second, and the second feeds the third. If you make an arithmetic slip early, write your number clearly and use it consistently: CIE awards 'error carried forward' (ecf) marks for correct method even when an earlier number is wrong. Students who panic and start over usually run out of time and lose everything.

If you want a single sheet that groups every formula by topic, [the IGCSE Physics formulas explained article](/igcse-physics-formulas-explained) gives you the printable version, with worked mini-examples for each one.