ESAT Physics equations

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• Acceleration from a change in velocitya = (v − u) ÷ t
• suvat: final velocity from u, a and tv = u + at
• suvat: displacement from u, a and ts = ut + ½at²
• suvat: the equation with no time in itv² = u² + 2as
• suvat: displacement from the average velocitys = ½(u + v)t
• Gradient and area of a velocity–time graphGradient is acceleration; area under the line is displacement.
• Newton’s second lawResultant force = mass × acceleration (F = ma).
• WeightW = mg
• Momentump = mv. In a collision with no external force, total momentum is conserved.
• Force and change of momentumF = Δ(mv) ÷ Δt: force is the rate of change of momentum.
• Moment of a forceForce × perpendicular distance from the pivot to the line of the force.
• Hooke’s lawF = kx, up to the limit of proportionality.
• Energy stored in a stretched spring½kx²
• Kinetic energy½mv²
• Change in gravitational potential energymgΔh
• Work done by a forceForce × distance moved in the direction of the force.
• PowerEnergy transferred ÷ time (P = E/t).
• EfficiencyUseful energy output ÷ total energy input (× 100 for a percentage).
• Densityρ = m ÷ V
• Pressurep = F ÷ A
• Pressure at depth h in a liquid of density ρp = ρgh (plus the pressure at the surface, if asked for the total).
• Specific heat capacity equationΔE = mcΔθ
• Specific latent heat equationE = mL
• Gas at constant temperature (fixed mass)pV = constant, so p₁V₁ = p₂V₂.
• Wave speedv = fλ
• Period and frequencyT = 1/f
• Refractive indexn = c ÷ v, the speed of light in a vacuum over its speed in the material.
• Snell’s lawn₁ sin θ₁ = n₂ sin θ₂
• Charge and currentQ = It
• Potential difference, current and resistanceV = IR
• Electrical power, three waysP = IV = I²R = V²/R
• Energy transferred by a charge moving through a p.d.E = QV
• Total resistance in seriesR = R₁ + R₂ + …
• Total resistance in parallel1/R = 1/R₁ + 1/R₂ + …
• Ideal transformerVp/Vs = Np/Ns, and VpIp = VsIs (power in = power out).
• Force on a wire carrying current I in a field B (at right angles)F = BIL
• An alpha particle2 protons and 2 neutrons: a helium nucleus, charge +2.
• A beta-minus particleA fast electron, emitted when a neutron in the nucleus changes into a proton.
• Half-lifeThe time for the number of undecayed nuclei (or the activity) to fall to half.
• Speed of light in a vacuumAbout 3.0 × 10⁸ m/s