IGCSE Physics: Motion, Forces and Energy — Revision Notes

Condensed for the final weeks. For the full explanation, use the Motion, Forces and Energy study guide.

Equations to know cold

Quantity	Equation
Average speed	speed = distance / time
Velocity	speed in a given direction (a vector; same formula as speed, v = s/t, but with a direction attached)
Acceleration (Supplement)	a = Δv / Δt
Weight	W = mg
Density	ρ = m / V
Hooke’s law (Supplement)	F = kx (extension x, sometimes written e) (within the limit of proportionality)
Newton’s second law (Supplement)	F = ma
Momentum (Supplement)	p = mv
Impulse (Supplement)	impulse = FΔt = Δp
Work done	W = Fd
Power	P = W/t = ΔE/t
Pressure	p = F/A
Pressure in a liquid (Supplement)	Δp = ρgΔh

Graphs — the part everyone under-revises

Distance–time graph: gradient = speed. A curved (steepening) line means increasing speed; flat means stationary.

Speed–time graph: gradient = acceleration. Area under the graph = distance travelled — this comes up constantly and is worth practising as its own skill, separate from reading the gradient.

Terminal velocity (Supplement): an object falling through air/liquid accelerates until air resistance balances weight; from that point resultant force = 0, so it continues at constant (terminal) velocity — a flat section on a speed–time graph.

Speed vs velocity

Speed is a scalar — magnitude only. Velocity is speed in a given direction — a vector. An object can have constant speed but changing velocity if its direction is changing (e.g. moving at constant speed around a bend), and this changing velocity is itself an acceleration.

Mass vs weight — the single most common mix-up

• Mass is the amount of matter in an object. Measured in kg. The same everywhere.
• Weight is the pull of gravity on that mass — a force, measured in newtons (N). Changes if gravitational field strength changes (e.g. weight on the Moon is about 1/6 of weight on Earth; mass is unchanged).
• Link them with g = W/m, so W = mg. On Earth’s surface, g ≈ 9.8 N/kg (equivalently, free-fall acceleration ≈ 9.8 m/s²).

Forces

• Newton’s first law: an object stays at rest, or moving at constant velocity in a straight line, unless a resultant (unbalanced) force acts on it.
• Resultant force = the single force with the same effect as all the forces acting together. If forces are balanced, resultant = 0.
• Hooke’s law (Supplement): extension x is directly proportional to force, up to the limit of proportionality — beyond that limit, the load–extension graph stops being a straight line.
• Moment of a force = force × perpendicular distance from the pivot. Principle of moments: for a body in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments. Note this is about moments only — a body is in equilibrium when there is no resultant force AND no resultant moment; balanced moments alone are not enough if the forces don’t also balance.
• Centre of gravity: the single point where an object’s whole weight can be considered to act. A wider base and lower centre of gravity make an object more stable — this is worth being able to explain, not just state.

Momentum (Supplement only)

p = mv
Δp = FΔt   (impulse = change in momentum)
F = Δp/Δt  (resultant force = rate of change of momentum)

Conservation of momentum: in a closed system with no external forces, total momentum before a collision/explosion = total momentum after. Always define a positive direction first, then treat velocities in the opposite direction as negative — this is where marks are lost, not in the arithmetic.

Energy, work and power

• Principle of conservation of energy: energy cannot be created or destroyed, only transferred from one store to another (or the same store, redistributed between objects).
• Work done, W = Fd — the force must act in the direction of motion; only that component does work.
• Kinetic energy (Supplement): KE = ½mv². Gravitational potential energy (Supplement): GPE = mgh (change in height).
• Sankey diagrams (Supplement) show energy input on the left, useful and wasted output on the right, with arrow width proportional to energy — read them by comparing arrow widths, not just labels.
• Power, P = W/t = ΔE/t — the rate of doing work, or the rate of energy transfer. Units: watts (W), 1 W = 1 J/s.
• Efficiency (Supplement) = useful energy output / total energy input (as a fraction or percentage) — never more than 100%.

Pressure

• p = F/A — for the same force, a smaller area gives a larger pressure. This is the idea behind sharp blades (small contact area) and snowshoes (large contact area).
• Pressure in a liquid (Supplement): Δp = ρgΔh — pressure increases with depth and with the liquid’s density, and does not depend on the shape or width of the container.

Common mistakes

• Writing “weight = mass” or using kg for weight — weight is a force, always in newtons.
• Treating speed and velocity as interchangeable — velocity is speed in a given direction (a vector); a constant speed with changing direction is still an acceleration.
• Reading a speed–time graph’s gradient as distance, or its area as speed — gradient is acceleration, area is distance.
• Forgetting that momentum is a vector: opposite-direction velocities must be given opposite signs before adding.
• Quoting Hooke’s law without the “within the limit of proportionality” condition — beyond that limit F = kx no longer holds.
• Treating efficiency as if it could exceed 100%, or forgetting it must be expressed as useful ÷ total, not total ÷ useful.

Examiner report insight

• Momentum conservation from rest: if two objects start at rest and then move apart (e.g. two trolleys pushed apart by a spring), the total momentum before and after is zero – don’t assume this is a collision where the objects “stick together”; instead, the two final momenta must be equal and opposite.
• Instantaneous gradient from a curve: finding an acceleration (or any rate) at one specific instant on a curved graph needs a tangent drawn and measured at that exact point – calculating a change in v over a change in t between two different points on the curve does not give the same answer.
• Newton’s first law: no resultant force means an object continues at constant velocity, not that it is at rest – a stationary object with no resultant force stays stationary, but a moving one keeps moving at the same speed and direction.

Source: Cambridge International, 0625 Physics Principal Examiner Report, June 2024 series, Papers 21, 23, 31, 41 (verified 2026-09-02).

Self-test

1. A car’s speed–time graph is a straight line from (0 s, 0 m/s) to (10 s, 20 m/s). Find the acceleration and the distance travelled.
2. State the difference between mass and weight, including units.
3. A trolley of mass 2 kg moving at 3 m/s collides with a stationary 1 kg trolley and they stick together. Find their common velocity.
4. Define efficiency and explain why it can never exceed 100%.
5. Explain, using p = F/A, why a drawing pin has a sharp point.

Answers: 1. Acceleration = Δv/Δt = 20/10 = 2 m/s². Distance = area under graph = ½ × 10 × 20 = 100 m. 2. Mass is the amount of matter (kg), the same everywhere; weight is the gravitational force on that mass (N), which varies with gravitational field strength. 3. Momentum conserved: (2×3) + (1×0) = (2+1)×v → v = 2 m/s. 4. Efficiency = useful energy output ÷ total energy input; some energy is always wasted (usually as heat) in any real process, so useful output can never exceed total input. 5. A small contact area at the point, for a given force, produces a much larger pressure (p = F/A), allowing it to penetrate the surface.