Free reference guide · VCE
Worked examples: VCE Physics Formula Sheet
Read the equations on the 2026 VCAA Physics sheet with original examples in motion, fields, circuits, waves and relativity.
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Formula index with worked examples
Motion · average velocity and acceleration
Formula or reference: v = Δs/Δt. a = Δv/Δt.
Units and conditions: Displacement in m, time in s, velocity in m/s and acceleration in m/s².
Worked example: A displacement of 12 m in 4 s gives average velocity 3 m/s. A velocity increase of 6 m/s in 4 s gives average acceleration 1.5 m/s².
Motion · constant acceleration
Formula or reference: v = u + at. s = ut + at²/2 = vt − at²/2 = (u + v)t/2. v² = u² + 2as.
Units and conditions: Take signed values along one axis. Use m and s.
Worked example: For u = 2 m/s, a = 2 m/s² and t = 3 s, v = 8 m/s and s = 15 m by any of the displacement forms. Also, 8² = 2² + 2 × 2 × 15.
Forces · Newton’s second law
Formula or reference: ΣF = ma
Units and conditions: Net force in N, mass in kg and acceleration in m/s².
Worked example: A 3 kg cart with net force 12 N accelerates at 4 m/s² in the direction of that force.
Motion · uniform circular motion
Formula or reference: v = 2πr/T. Fnet = mv²/r.
Units and conditions: Period in s, speed in m/s, radius in m and inward net force in N.
Worked example: A 2 kg mass takes 2 s per circle of radius 1 m. Its speed is π m/s and its inward net force is about 19.7 N.
Forces · Hooke’s law
Formula or reference: F = −kx
Units and conditions: Displacement in m and stiffness in N/m. The minus sign denotes the restoring direction.
Worked example: For k = 80 N/m and x = +0.10 m, the spring’s restoring force is −8.0 N.
Energy · gravitational potential energy change
Formula or reference: ΔEg = mgΔh near Earth’s surface
Units and conditions: Mass in kg, height change in m and energy in J.
Worked example: Lifting 2 kg by 3 m increases gravitational potential energy by 2 × 9.81 × 3 ≈ 58.9 J.
Energy · kinetic energy
Formula or reference: Ek = mv²/2
Units and conditions: Use mass in kg and speed in m/s to obtain J.
Worked example: A 4 kg object at 3 m/s has kinetic energy 18 J.
Gravity · force and field
Formula or reference: Fg = Gm₁m₂/r². g = GM/r².
Units and conditions: Use distance between centres in m. Field strength is in N/kg.
Worked example: If GM = 36 m³/s² and r = 3 m, g = 4 N/kg and the gravitational force on 2 kg is 8 N.
Motion · impulse
Formula or reference: FΔt = mΔv for average net force F
Units and conditions: Impulse in N s, mass in kg and velocity in m/s.
Worked example: A 0.25 kg ball changes velocity from +8 to −4 m/s. Its impulse is −3 N s, opposite the initial direction.
Motion · momentum
Formula or reference: p = mv
Units and conditions: Momentum in kg m/s, with the same direction as velocity.
Worked example: A 0.50 kg ball moving west at 6 m/s has momentum 3.0 kg m/s west.
Energy · elastic potential energy
Formula or reference: Eₛ = kx²/2
Units and conditions: Spring stiffness in N/m, extension in metres and energy in joules.
Worked example: Stretching a spring of stiffness 80 N/m by 0.10 m stores 0.40 J.
Relativity · time dilation
Formula or reference: t = γt₀, with γ = 1/√(1 − v²/c²).
Units and conditions: Use consistent speed units. t₀ is the proper time.
Worked example: At v = 0.60c, γ = 1.25. A proper interval of 4.0 μs corresponds to 5.0 μs in the frame in which the clock moves.
Relativity · length contraction
Formula or reference: L = L₀/γ
Units and conditions: L₀ is measured in the object’s rest frame. Contraction is along the direction of motion.
Worked example: A 10 m object moving at 0.60c measures 10/1.25 = 8 m along its motion.
Relativity · energy
Formula or reference: E₀ = mc². Etotal = Ek + E₀ = γmc². Ek = (γ − 1)mc².
Units and conditions: Use joules or another consistent energy unit across all terms.
Worked example: At γ = 1.25, an object of rest energy 8.0 J has total energy 10 J and kinetic energy 2.0 J.
Electric fields · charged plates
Formula or reference: E = V/d
Units and conditions: Use potential difference in V and plate spacing in m. Field magnitude is in V/m.
Worked example: A 60 V difference across a 0.020 m gap gives 3000 V/m, neglecting edge effects.
Electric fields · energy transfer
Formula or reference: mv²/2 = qV for a particle starting at rest that gains kinetic energy qV.
Units and conditions: Use J, kg, C and V. Choose the sign or magnitude so qV represents the kinetic energy gained.
Worked example: A particle of mass 1.0 × 10⁻²⁶ kg gains 8.0 × 10⁻¹⁸ J crossing a potential difference. Its nonrelativistic speed is 4.0 × 10⁴ m/s.
Electric fields · point charge and electric force
Formula or reference: E = kQ/r². F = qE.
Units and conditions: The point-charge field magnitude uses |Q|. Use SI units and determine direction separately.
Worked example: If k|Q| = 36 N m²/C at r = 3 m, E = 4 N/C. A +2.0 μC test charge feels 8.0 μN along the field.
Electric forces · Coulomb’s law
Formula or reference: F = k|q₁q₂|/r²
Units and conditions: Use C, m and N. Like charges repel and unlike charges attract.
Worked example: If k|q₁q₂| = 0.060 N m² and r = 0.30 m, the magnitude is 0.67 N.
Magnetic forces · moving charge
Formula or reference: F = |q|vB when velocity is perpendicular to B.
Units and conditions: Use C, m/s and T to obtain N.
Worked example: A charge of magnitude 2.0 μC moving at 400 m/s across a 0.50 T field feels a force of 4.0 × 10⁻⁴ N.
Magnetic forces · current-carrying wire
Formula or reference: F = nIℓB for n perpendicular active lengths whose forces add.
Units and conditions: Use A, m and T. Count only lengths that contribute in the direction being considered.
Worked example: Three active 0.20 m lengths carrying 2 A in a 0.50 T field contribute 0.60 N.
Magnetic forces · orbit radius
Formula or reference: r = mv/(|q|B) for perpendicular motion.
Units and conditions: Use kg, m/s, C and T to obtain m.
Worked example: If mv/|q| = 0.12 T m and B = 0.40 T, r = 0.30 m.
Circuits · current and power
Formula or reference: I = V/R. P = VI.
Units and conditions: Use V, Ω, A and W.
Worked example: A 6 Ω resistor across 12 V draws 2 A and dissipates 24 W.
Circuits · resistors in series and parallel
Formula or reference: Series: RT = R₁ + R₂ + …. Parallel: 1/RT = 1/R₁ + 1/R₂ + ….
Units and conditions: Resistance in Ω.
Worked example: A 6 Ω and 3 Ω pair gives 9 Ω in series or 2 Ω in parallel.
Electricity · ideal transformer
Formula or reference: N₁/N₂ = V₁/V₂ = I₂/I₁
Units and conditions: Turn counts are unitless. Use consistent voltage and current measures.
Worked example: A 400-turn primary and 100-turn secondary take 24 V and 0.50 A on the primary to 6 V and 2 A on the secondary.
Electricity · RMS voltage and current
Formula or reference: VRMS = Vpeak/√2. IRMS = Ipeak/√2 for sinusoids.
Units and conditions: Use V for voltage and A for current.
Worked example: A 20 V peak and 4 A peak give approximately 14.1 V RMS and 2.83 A RMS.
Electricity · induction and magnetic flux
Formula or reference: ε = −NΔΦ/Δt. Φ = B⊥A.
Units and conditions: Flux in Wb, area in m², normal field in T and EMF in V.
Worked example: If a 20-turn loop’s normal field increases by 0.10 T over 0.05 s across area 0.020 m², ΔΦ = 0.0020 Wb per turn and |ε| = 0.80 V.
Electricity · line losses
Formula or reference: Vdrop = IlineRline. Ploss = Iline²Rline.
Units and conditions: Use A, Ω, V and W.
Worked example: A 3 A line current through 2 Ω of line resistance drops 6 V and dissipates 18 W.
Waves · wave speed
Formula or reference: v = fλ
Units and conditions: Speed in m/s, frequency in Hz and wavelength in m.
Worked example: A 2 Hz wave with wavelength 1.5 m travels at 3 m/s.
Waves · interference
Formula or reference: In-phase sources: constructive at path difference nλ, destructive at (n + ½)λ.
Units and conditions: n is an integer and the path difference uses the same length unit as λ.
Worked example: For λ = 0.20 m, path difference 0.40 m is constructive and 0.30 m is destructive.
Waves · fringe spacing
Formula or reference: Δx = λL/d when L ≫ d.
Units and conditions: Use metres for wavelength, screen distance, slit spacing and fringe spacing.
Worked example: For λ = 600 nm, L = 2.0 m and d = 0.30 mm, Δx = 0.0040 m.
Light · photoelectric effect
Formula or reference: Ek,max = hf − φ when hf ≥ φ.
Units and conditions: Keep photon energy and work function in the same units.
Worked example: A 5.0 eV photon incident on a surface with work function 2.0 eV gives maximum electron kinetic energy 3.0 eV.
Light · photon energy
Formula or reference: E = hf = hc/λ
Units and conditions: With h in J s, use f in Hz and λ in m to obtain joules.
Worked example: A photon of frequency 5.0 × 10¹⁴ Hz has energy about 3.32 × 10⁻¹⁹ J.
Matter and light · wavelength and momentum
Formula or reference: Photon momentum p = h/λ. De Broglie wavelength λ = h/p.
Units and conditions: Use h in J s, p in kg m/s and λ in m.
Worked example: A 600 nm photon has p ≈ 1.10 × 10⁻²⁷ kg m/s. A particle with that momentum has a 600 nm de Broglie wavelength.
Units · mass and energy conversions
Formula or reference: 1 tonne = 10³ kg. 1 kWh = 3.6 × 10⁶ J.
Units and conditions: Match the unit required by the equation before substitution.
Worked example: A mass of 0.40 tonnes is 400 kg. An energy use of 0.50 kWh is 1.8 × 10⁶ J.
What to work out beyond the sheet
Sketch each reference frame and identify the proper quantity before deciding which time or length to divide or multiply by γ.
Subject resources · Official past papers · ATAR calculator guide