Cambridge IGCSE Physics Formula List: Motion, Forces, Energy

The single most useful thing to understand about Cambridge IGCSE Physics (0625) is that, unlike Edexcel, Cambridge does not hand you a formula sheet in the exam. There is a short list of equations you are expected to recall, and a few relationships you can derive on the spot from a graph or a definition. If you walk in expecting a printed sheet, you will waste minutes and lose easy marks.

So the smart approach is to sort every relationship into three buckets:

• Recall exactly: the compact core equations below. These come up on almost every paper.
• Derive from a graph: gradient of a speed-time graph is acceleration, area under it is distance. You are not memorising a formula, you are reading a picture.
• Build from a definition: density is mass per unit volume, pressure is force per unit area. If you know what the quantity means, the equation writes itself.

One accuracy note that sharpens your revision: the classic full SUVAT set (for example $v^2 = u^2 + 2as$) belongs to Edexcel IGCSE (4PH1) and to A-Level, not to Cambridge 0625. On 0625 you use $v = u + at$ only through the acceleration definition and the graph method. Memorising equations that are not on your syllabus is a common way strong students waste time. For the fuller topic treatment, see the IGCSE physics forces and motion guide.

Average speed

is distance travelled divided by time taken:

$$v = \frac{s}{t}$$

Be strict about the words. Speed is a scalar, velocity is speed with a direction. In numerical questions the arithmetic is identical, but a describe or define question will only give the mark if you say velocity is a vector.

Acceleration

is the rate of change of velocity:

$$a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}$$

Here $u$ is the starting (initial) velocity and $v$ is the final velocity. Deceleration is just negative acceleration, so a value like $-2\ \text{m/s}^2$ is a correct answer, not a mistake.

The part students underuse is the speed-time graph, which replaces two separate formulas:

• The gradient of a speed-time graph gives the acceleration.
• The area under a speed-time graph gives the distance travelled.

So for a trapezium-shaped graph, split it into a triangle and a rectangle, find each area, and add them. That single technique answers a large share of the motion marks on Paper 4 without you memorising anything extra. On the Earth, free-fall acceleration is $g \approx 9.8\ \text{m/s}^2$ (many mark schemes accept $10\ \text{m/s}^2$; check the value stated in the question).

This is the densest formula group on the syllabus. Learn them as a family.

• Newton's second law, resultant force equals mass times acceleration: $$F = ma$$
• Weight, the pull of gravity on a mass: $$W = mg$$
• Density, mass per unit volume: $$\rho = \frac{m}{V}$$
• Pressure, force per unit area: $$p = \frac{F}{A}$$
• Pressure in a liquid column (Extended): $$p = \rho g h$$
• Moment of a force about a pivot: $$M = F \times d$$ where $d$ is the perpendicular distance from the pivot to the line of action.
• Hooke's law, force proportional to extension for a spring: $$F = kx$$
• Momentum (Extended): $$p = mv$$

Two relationships are worth stating as principles, not just formulas. The principle of moments says that for a balanced object, total clockwise moment equals total anticlockwise moment. And the conservation of momentum says total momentum before a collision equals total momentum after, provided no external force acts. Examiners love a collision question where you set momentum before equal to momentum after and solve for one unknown.

A frequent trap: in a moments question, $d$ must be the perpendicular distance, and in $p = \frac{F}{A}$ the area must be in $\text{m}^2$, not $\text{cm}^2$. For more of these silent point-losers, read the calculations students get wrong.

These four relationships tie the whole mechanics topic together, because energy is conserved and you can track it from one form to another.

• Kinetic energy, the energy of a moving mass: $$E_k = \frac{1}{2}mv^2$$
• Change in gravitational potential energy when height changes: $$\Delta E_p = mg\,\Delta h$$
• Work done by a force, which equals the energy transferred: $$W = Fd$$
• Power, the rate of doing work or transferring energy: $$P = \frac{W}{t} = \frac{E}{t}$$

Efficiency

is not a joules formula but a ratio, usually asked as a percentage:

$$\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%$$

The conceptual key is conservation. When a ball falls, gravitational PE turns into KE; ignoring air resistance, $mg\,\Delta h = \frac{1}{2}mv^2$. Notice the mass cancels, which is why the equation predicts the same landing speed for a heavy and a light object dropped from the same height. Setting one energy equal to another is the move that unlocks the hardest six-mark energy questions.

Notice too that $E_k$ depends on $v^2$: double the speed and the kinetic energy quadruples. This is exactly the reasoning examiners want in braking-distance and safety questions.

Real Paper 4 questions rarely test one formula in isolation. Here is a typical multi-step item.

Question.

A trolley of mass $2.0\ \text{kg}$ starts from rest and is pushed by a constant resultant force of $6.0\ \text{N}$ for $4.0\ \text{s}$ along a level track. Find (a) the acceleration, (b) the final speed, (c) the kinetic energy at that speed, and (d) the average power delivered.

Step 1, acceleration.

Use $F = ma$, rearranged to $a = \frac{F}{m}$:

$$a = \frac{6.0}{2.0} = 3.0\ \text{m/s}^2$$

Step 2, final speed.

Starting from rest means $u = 0$, so from $a = \frac{v - u}{t}$ we get $v = at$:

$$v = 3.0 \times 4.0 = 12\ \text{m/s}$$

Step 3, kinetic energy.

Use $E_k = \frac{1}{2}mv^2$:

$$E_k = \frac{1}{2} \times 2.0 \times 12^2 = \frac{1}{2} \times 2.0 \times 144 = 144\ \text{J}$$

Step 4, average power.

The trolley gained $144\ \text{J}$ in $4.0\ \text{s}$, so from $P = \frac{E}{t}$:

$$P = \frac{144}{4.0} = 36\ \text{W}$$

Notice how one answer feeds the next, and how each line states the equation, substitutes, then gives a number with a unit. That layout, equation then substitution then value with unit, is exactly what earns method marks even when the final number slips. For the wider habit set, see IGCSE physics formulas explained.