NCEA L1 Physics & ESS cheat sheet

Speed is distance ÷ time (scalar); velocity adds direction (vector). Average speed = total distance ÷ total time, not the average of separate speeds.

Acceleration a = Δv ÷ Δt, measured in m s⁻². On a velocity–time graph, gradient = acceleration and area under the line = displacement.

Newton's second law: F_net = ma. Weight is a force, W = mg, with g ≈ 9.8 N kg⁻¹ near Earth's surface; mass in kg does not change with location.

Forces are vectors: add tip-to-tail. A body at constant velocity (or at rest) has zero net force, so friction balances the driving force.

Work W = Fd cos θ (joules); power P = W ÷ t = Fv (watts). Energy is conserved but transfers are never 100% useful.

Kinetic energy E_k = ½mv²; gravitational potential energy change ΔE_p = mgΔh. In a frictionless system E_k gained = E_p lost.

Ohm's law V = IR holds for ohmic resistors at constant temperature; resistance R = V ÷ I in ohms (Ω).

Series: same current, voltages add, R_total = R₁ + R₂. Parallel: same voltage, currents add, 1/R_total = 1/R₁ + 1/R₂.

Electrical power P = VI = I²R = V²/R; energy used E = Pt, billed in kilowatt-hours (1 kWh = 3.6 × 10⁶ J).

Earth's interior layers by composition: crust, mantle, outer core (liquid iron–nickel), inner core (solid). S-waves cannot pass through the liquid outer core, which is evidence for it.

Tectonic plates move a few centimetres per year. Divergent boundaries create new crust (mid-ocean ridges, rift valleys); convergent boundaries destroy or thicken crust (trenches, volcanoes, fold mountains); transform boundaries slide past (earthquakes).

The rock cycle links igneous (cooled magma/lava), sedimentary (deposited and lithified layers) and metamorphic (heat and pressure) rocks; melting, weathering and erosion move material between them.

Earthquakes release stored elastic energy at a focus; the epicentre is the point on the surface above it. P-waves arrive first (fast, compressional); S-waves follow (slower, transverse).

The Earth's tilt of about 23.5° to its orbital plane causes seasons; the hemisphere tilted toward the Sun receives more direct sunlight and longer days.

Day and night come from Earth's rotation on its axis (about 24 hours); a year is one orbit around the Sun (about 365.25 days), which is why leap years exist.

The Moon orbits Earth roughly every 27.3 days; the same side always faces Earth because its rotation period equals its orbital period (tidal locking).

Phases of the Moon depend on the angle between Sun, Earth and Moon; a solar eclipse needs the Moon between Sun and Earth (new Moon), a lunar eclipse needs Earth between them (full Moon).

The Sun is a main-sequence star fusing hydrogen to helium in its core; the Solar System's planets orbit in nearly the same plane, and the inner planets are rocky while the outer planets are gas/ice giants.