These four equations apply when acceleration is constant. u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.

A projectile moves under gravity alone after being launched. The horizontal and vertical motions are independent.

• Horizontal: constant velocity (no acceleration) — use s = vt
• Vertical: uniform acceleration due to gravity (g = 10 m/s²)
• At the maximum height, the vertical velocity = 0
• Time of flight: t_total = 2u sinθ / g (for projectile at angle θ)

Momentum = mass × velocity (p = mv). Unit: kg·m/s. It is a vector quantity.
Impulse = Force × time = change in momentum (Ft = mv − mu).
Law of conservation of momentum: In the absence of external forces, total momentum before = total momentum after a collision.

Mechanical Advantage (MA) = Load ÷ Effort
Velocity Ratio (VR) = Effort distance ÷ Load distance
Efficiency = (MA ÷ VR) × 100%

Pressure = Force / Area (P = F/A). Unit: Pascal (Pa) = N/m²
Pressure in a liquid: P = ρgh (density × g × depth). Pressure increases with depth and with liquid density.

Archimedes' Principle: When a body is wholly or partially immersed in a fluid, it experiences an upthrust (buoyant force) equal to the weight of fluid displaced.

Upthrust = Weight of fluid displaced = ρ_fluid × V_submerged × g

• Sound is a longitudinal mechanical wave — it requires a medium to travel.
• Speed of sound: fastest in solids, slower in liquids, slowest in gases.
• Sound travels at approximately 340 m/s in air at room temperature.
• Pitch depends on frequency. High frequency = high pitch.
• Loudness depends on amplitude. Large amplitude = loud sound.
• Quality (timbre) depends on the waveform — distinguishes different instruments.

Echo: Reflection of sound from a hard surface. For an echo to be heard separately, the reflecting surface must be at least 17 m away (so the reflected sound reaches the ear at least 0.1 s after the original).

Resonance: When a body is forced to vibrate at its own natural frequency — the amplitude becomes very large. Examples: Soldiers break step on bridges to avoid resonance.

Human hearing range: 20 Hz to 20,000 Hz (20 kHz).
Infrasound: Below 20 Hz. Ultrasound: Above 20 kHz (used in medicine, sonar).

Laws of Reflection:
1. The angle of incidence equals the angle of reflection (i = r).
2. The incident ray, reflected ray, and normal all lie in the same plane.

Refraction: change in direction of light as it passes from one medium to another due to change in speed.
Light bends towards the normal when going from less dense to more dense medium (e.g. air → glass).
Light bends away from the normal when going from more dense to less dense (e.g. glass → air).

Total Internal Reflection (TIR): occurs when light travels from a denser to less dense medium and the angle of incidence exceeds the critical angle. Applications: optical fibres, periscopes, diamonds, binoculars.

There are two types of charge: positive (+) and negative (−). Like charges repel; unlike charges attract.
The SI unit of charge is the Coulomb (C).
Coulomb's Law: F = kq₁q₂/r² — force between charges is proportional to the product of charges and inversely proportional to distance squared.

Ohm's Law: Voltage is directly proportional to current at constant temperature. V = IR
V = Voltage (Volts, V) · I = Current (Amperes, A) · R = Resistance (Ohms, Ω)

• Like poles repel; unlike poles attract.
• Magnetic field lines run from North to South outside a magnet.
• A current-carrying conductor produces a circular magnetic field around it.
• The right-hand grip rule: grip the wire with thumb pointing in direction of conventional current → fingers curl in direction of field.

Faraday's Law: An EMF is induced in a conductor whenever the magnetic flux through it changes.
Lenz's Law: The induced current opposes the change causing it.

Specific Heat Capacity (c): Heat needed to raise 1 kg of a substance by 1°C (or 1 K).
Q = mcΔT where m = mass, c = specific heat capacity, ΔT = temperature change.
Specific heat capacity of water = 4,200 J/kg/K (highest common value — explains why water is a good coolant).

Latent Heat (L): Heat needed to change the state of a substance at constant temperature.
Q = mL. Latent heat of fusion: solid → liquid. Latent heat of vaporisation: liquid → gas.

Half-life: Time taken for half the radioactive atoms in a sample to decay. After n half-lives, the amount remaining = N₀ × (½)ⁿ.

Nuclear fission: Heavy nucleus splits into smaller fragments + energy (e.g. uranium-235). Used in nuclear reactors and atomic bombs.
Nuclear fusion: Two light nuclei combine to form a heavier nucleus + energy (e.g. hydrogen → helium). Occurs in stars/sun. Fusion releases more energy per unit mass than fission.

Conductors: Allow free flow of electrons (copper, aluminium).
Insulators: Do not allow electron flow (rubber, wood, plastic).
Semiconductors: Conductivity between conductors and insulators — conductivity increases with temperature. Examples: Silicon, Germanium.

Diode (p-n junction): Allows current to flow in one direction only. Used in rectification (converting AC to DC).
Half-wave rectification: one diode — only one half-cycle passes.
Full-wave rectification: four diodes (bridge rectifier) — both half-cycles used.

The photoelectric effect: When light of sufficiently high frequency shines on a metal surface, electrons are emitted. Explained by Einstein using the particle (photon) model of light.

• Threshold frequency: minimum frequency of light needed to emit electrons.
• Increasing intensity increases the number of electrons but NOT their energy.
• Increasing frequency increases the kinetic energy of emitted electrons.
• Photon energy: E = hf (h = Planck's constant = 6.63 × 10⁻³⁴ J·s)

You've now covered all major WAEC and JAMB Physics topics. Take the 100-question timed CBT practice to see your score and get a personalised breakdown by section.