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Secondary physics

Formula sheet

Pick the quantity you do not know, type the others, and the sheet rearranges the equation. Units stay in SI unless a symbol says otherwise.

Conversions that cost marks

Mechanics

Motion

Average speed

v = s / t

Use for a whole journey. s is distance travelled. It is not a vector.

v
average speed
m/s
s
distance
m
t
time
s

Acceleration

a = (v − u) / t

Change in velocity over time. A negative value means a deceleration if forward is positive.

a
acceleration
m/s²
v
final velocity
m/s
u
initial velocity
m/s
t
time
s

Velocity after time

v = u + at

Constant acceleration in a straight line. Same relation as the definition of a.

v
final velocity
m/s
u
initial velocity
m/s
a
acceleration
m/s²
t
time
s

Displacement

s = ut + (1/2)at²

How far it travels under constant acceleration. From rest, this becomes s = (1/2)at².

s
displacement
m
u
initial velocity
m/s
a
acceleration
m/s²
t
time
s

Velocity without time

v² = u² + 2as

When time is not given. The solver returns the positive root.

v
final speed
m/s
u
initial speed
m/s
a
acceleration
m/s²
s
displacement
m
Forces

Weight

W = mg

The gravitational force on a mass. On Earth in this course, g = 10 N/kg.

W
weight
N
m
mass
kg
g
gravitational field strength
N/kg

Newton’s second law

F = ma

F is the resultant force, in the direction of a. Balanced forces mean F = 0 and a = 0.

F
resultant force
N
m
mass
kg
a
acceleration
m/s²

Hooke’s law

F = kx

A spring or wire within its limit of proportionality. x is the extension.

F
force
N
k
spring constant
N/m
x
extension
m
Energy, work and power

Kinetic energy

Ek = (1/2)mv²

The energy of a moving mass. Doubling the speed multiplies the energy by four.

Ek
kinetic energy
J
m
mass
kg
v
speed
m/s

Gravitational potential energy

Ep = mgh

The change when a mass moves vertically through height h. Zero can be anywhere convenient.

Ep
gravitational energy
J
m
mass
kg
g
gravitational field strength
N/kg
h
height change
m

Work done

W = Fs

A force moving through a distance along its own direction. The unit is the joule.

W
work done
J
F
force
N
s
distance along the force
m

Power

P = E / t

The rate of energy transfer. Also P = W / t and, for a steady force, P = Fv.

P
power
W
E
energy transferred
J
t
time
s

Efficiency

efficiency = (useful / total) × 100%

Both energies must be in the same unit. The answer here is a percentage.

η
efficiency
%
useful
useful energy output
J
total
total energy input
J
Momentum

Momentum

p = mv

State the direction. The unit kg m/s is the same as the newton second.

p
momentum
kg m/s
m
mass
kg
v
velocity
m/s

Impulse

impulse = Ft = Δp

Use a constant force, or the average force, over the contact time.

Ft
impulse
N s
F
force
N
t
time
s

Waves and light

Waves and sound

Wave speed

v = fλ

Any wave. If the medium fixes v, frequency and wavelength trade off.

v
wave speed
m/s
f
frequency
Hz
λ
wavelength
m

Period and frequency

T = 1 / f

One complete oscillation. A frequency of 4 Hz means a period of 0.25 s.

T
period
s
f
frequency
Hz

Echo distance

d = vt / 2

d is the distance to the reflector. t is the time to go there and back.

d
distance to the wall
m
v
speed of sound
m/s
t
time for the echo
s

Simple pendulum

T = 2π√(L / g)

Small angles, roughly under 10°. The period does not depend on the mass of the bob.

T
period
s
L
length to the centre of the bob
m
g
gravitational field strength
m/s²
Light

Snell’s law from air

n = sin i / sin r

The incident ray is in air. i and r are from the normal, in degrees in this solver.

n
refractive index
—
i
angle of incidence
°
r
angle of refraction
°

Critical angle

sin c = 1 / n

From the denser medium into air. There is no critical angle the other way.

c
critical angle
°
n
refractive index
—

Thin converging lens

1/f = 1/u + 1/v

Real-is-positive. A negative v from the solver means a virtual image. Object must be beyond the focus for a real image.

f
focal length
cm
u
object distance
cm
v
image distance
cm

Electricity

Electricity

Ohm’s law

V = IR

For a resistor at constant temperature, V and I are proportional. R = V/I defines resistance even when they are not.

V
potential difference
V
I
current
A
R
resistance
Ω

Electrical power

P = IV

Also P = I²R and P = V²/R. A kilowatt is 1 000 W.

P
power
W
I
current
A
V
potential difference
V

Charge and current

Q = It

Charge in coulombs, current in amperes, time in seconds.

Q
charge
C
I
current
A
t
time
s

Series resistors

R = R1 + R2

One path for the current. Add more resistors the same way.

R
combined resistance
Ω
R1
first resistance
Ω
R2
second resistance
Ω

Two parallel resistors

1/R = 1/R1 + 1/R2

Do not forget to invert at the end. Two equal resistors in parallel halve.

R
combined resistance
Ω
R1
first resistance
Ω
R2
second resistance
Ω

Matter and heat

Heating

Specific heat capacity

E = mcΔθ

A temperature change with no change of state. Δθ is in °C or K; the difference is the same.

E
energy
J
m
mass
kg
c
specific heat capacity
J/kg °C
Δθ
temperature change
°C

Specific latent heat

E = mL

Melting or boiling, with no temperature change. L is larger for vaporising than for melting.

E
energy
J
m
mass that changes state
kg
L
specific latent heat
J/kg

Energy from a heater

E = Pt

Pair this with E = mcΔθ when a heater warms a substance and losses are ignored.

E
energy
J
P
power
W
t
time
s
Density and pressure

Density

ρ = m / V

Keep mass and volume in a matching pair: kg with m³, or g with cm³.

ρ
density
kg/m³
m
mass
kg
V
volume
m³

Pressure

P = F / A

Force perpendicular to the area. A larger area means a smaller pressure for the same force.

P
pressure
Pa
F
force
N
A
area
m²

Pressure in a liquid

P = hρg

Extra pressure at depth h, not including the atmosphere, unless the question adds it.

P
pressure due to the liquid
Pa
h
depth
m
ρ
density
kg/m³
g
gravitational field strength
N/kg