Equation deep-dives

Ek = 1/2 m v²

The half and the squared are two separate marks to lose — and most people lose at least one.

Ep = m g h

h is the CHANGE in height, and AQA uses g = 9.8 N/kg unless the question says otherwise.

Ee = 1/2 k e²

e is the EXTENSION, not the length, and it is squared: two separate marks to lose.

dE = m c d(theta)

The temperature CHANGE trips everyone — d(theta) is the difference, not the final temperature.

P = E / t and P = W / t

Power is energy per SECOND: minutes and kilowatts both have to be converted first.

efficiency = useful output energy transfer / total input energy transfer

The top line is the USEFUL output only, and an efficiency can never be more than 1 (100%).

V = I R and P = I² R

Two equations, one topic — and P = I^2 R needs the current squared, not doubled.

v = f x lambda

Almost every mark lost here is a unit conversion: kHz, MHz, cm and nm all need converting first.

rho = m / V

The unit tells you what to divide by what — and cm^3 vs m^3 is the classic trap.

F = m a

F is the RESULTANT force — add up the forces first, then use F = m a.

p = m v

Higher tier: in a collision, total momentum before = total momentum after. Track the whole system.

M = F d

d is the PERPENDICULAR distance from the pivot to the line of the force, and balance means clockwise = anticlockwise.

p = F / A

Area must be in m^2 — and 1 m^2 is 10 000 cm^2, not 100.

x = A cos(omega t) and a = -omega² x

The sign gives the direction: SHM acceleration always points back towards equilibrium.

a = v² / r = omega² r and F = m v² / r

Centripetal force is not an extra force; it is the resultant inward force supplied by real forces.

Q = Q₀ e^{−t / (R C)}

The booklet prints the charge form. The voltage form used in the applications follows from Q = C V for a fixed capacitor.

g = G M / r² and V = -G M / r

Field strength follows 1/r^2, potential follows 1/r, and gravitational potential is negative when zero is at infinity.

E = Q / (4 pi epsilon₀ r²) and V = Q / (4 pi epsilon₀ r)

Electric potential carries the sign of the source charge; field strength calculations often ask for magnitude only.

epsilon = N d(Phi) / d(t)

Faraday's law uses the rate of change of flux linkage, not just the magnetic flux.

N = N₀ e^{−lambda t} and T₁/2 = ln(2) / lambda

Keep time and decay constant in matching units; hours with per hour is just as valid as seconds with per second.

p V = n R T and 1/2 m <c²> = 3/2 k T

Temperature must be absolute, and the speed relationship uses mean square speed before you take the square root.

E = h f and lambda = h / p

Nanometres and electronvolts are the traps: convert to metres and joules before using the booklet equations.