Equations on the Formula Sheet

In the Edexcel GCSE Physics (1PH0) exam, you are given an equation sheet. The equations below will be provided — but you still need to know what they mean, when to use them, and how to rearrange them. Simply having the equation in front of you is not enough if you cannot apply it correctly.

---

Why This Lesson Matters

Many students assume that because these equations are "given", they do not need to revise them. This is a dangerous mistake. The equation sheet tells you the formula — it does NOT tell you:

• What each symbol means
• What units to use
• When to apply the equation
• How to rearrange it

You must be able to use every one of these equations fluently.

---

Force and Motion

Newton's Second Law

F = ma

Symbol	Quantity	Unit
F	Force (resultant)	Newtons (N)
m	Mass	Kilograms (kg)
a	Acceleration	m/s²

When to use it: When you know two of force, mass, or acceleration and need the third. Also used to find the resultant force when mass and acceleration are known.

Worked example: Calculate the resultant force needed to accelerate a 1500 kg car at 2 m/s².

F = ma = 1500 × 2 = 3000 N

---

Momentum

p = mv

Symbol	Quantity	Unit
p	Momentum	kg m/s
m	Mass	kg
v	Velocity	m/s

When to use it: Questions about collisions, explosions, or conservation of momentum. Remember: momentum is a vector — direction matters.

Worked example: A 0.5 kg ball moves at 8 m/s. Calculate its momentum.

p = mv = 0.5 × 8 = 4 kg m/s

---

Force and Change in Momentum

F = Δp / Δt (or F = (mv − mu) / t)

Symbol	Quantity	Unit
F	Force	Newtons (N)
Δp	Change in momentum	kg m/s
Δt	Time	Seconds (s)

When to use it: Questions about impact forces, crumple zones, airbags — anything that links force to how quickly momentum changes.

Worked example: A 70 kg person is brought to rest from 10 m/s in a car crash lasting 0.5 s. Calculate the average force.

Δp = mv − mu = 70 × 0 − 70 × 10 = −700 kg m/s

F = Δp / Δt = −700 / 0.5 = −1400 N (the negative sign indicates the force acts opposite to the direction of motion)

Exam Tip: Crumple zones and airbags work by increasing the time of impact (Δt). This reduces the force (F) for the same change in momentum (Δp). This is a very common 6-mark question topic.

---

Equations of Motion

Distance (uniform acceleration)

s = vt (where v is average velocity during uniform motion)

For uniform acceleration from rest, the more useful form is s = ½(u + v)t or the SUVAT equation:

Velocity–Displacement Equation

v² = u² + 2as

Symbol	Quantity	Unit
v	Final velocity	m/s
u	Initial velocity	m/s
a	Acceleration	m/s²
s	Distance	m

When to use it: When you have three of the four variables (v, u, a, s) and need to find the fourth — and time is NOT involved.

Worked example: A car accelerates from rest at 3 m/s² over a distance of 54 m. Calculate the final velocity.

v² = u² + 2as = 0² + 2 × 3 × 54 = 324

v = √324 = 18 m/s

Exam Tip: When using v² = u² + 2as, always check whether the object starts from rest (u = 0) or decelerates to rest (v = 0). This simplifies the calculation.

---

Springs and Elastic Deformation

Hooke's Law

F = kx

Symbol	Quantity	Unit
F	Force applied	Newtons (N)
k	Spring constant	N/m
x	Extension	Metres (m)

When to use it: For springs and materials that obey Hooke's law (linear region of a force–extension graph).

Worked example: A spring has a spring constant of 40 N/m and is stretched by 0.15 m. Calculate the force.

F = kx = 40 × 0.15 = 6 N

---

Elastic Potential Energy

E = ½kx²

Symbol	Quantity	Unit
E	Elastic potential energy	Joules (J)
k	Spring constant	N/m
x	Extension	Metres (m)

When to use it: To calculate the energy stored in a stretched or compressed spring.

Worked example: Calculate the energy stored in a spring with k = 40 N/m stretched by 0.15 m.

E = ½kx² = ½ × 40 × 0.15² = ½ × 40 × 0.0225 = 0.45 J

---

Thermal Energy

Specific Heat Capacity

ΔE = mcΔθ

Symbol	Quantity	Unit
ΔE	Change in thermal energy	Joules (J)
m	Mass	Kilograms (kg)
c	Specific heat capacity	J/(kg °C)
Δθ	Change in temperature	°C

When to use it: Heating or cooling a substance WITHOUT a change of state.

Worked example: Calculate the energy needed to heat 2 kg of water from 20°C to 100°C. (c for water = 4200 J/(kg °C))

ΔE = mcΔθ = 2 × 4200 × (100 − 20) = 2 × 4200 × 80 = 672,000 J (672 kJ)

---

Specific Latent Heat

E = mL

Symbol	Quantity	Unit
E	Energy	Joules (J)
m	Mass	Kilograms (kg)
L	Specific latent heat	J/kg

When to use it: During a change of state (melting, boiling, freezing, condensing) — the temperature stays constant but energy is transferred.

Worked example: Calculate the energy needed to melt 0.5 kg of ice. (L for ice = 334,000 J/kg)

E = mL = 0.5 × 334,000 = 167,000 J (167 kJ)

Exam Tip: The key difference: use ΔE = mcΔθ when the temperature changes (no state change), and use E = mL when the state changes (temperature stays constant).

---

Pressure in Fluids

Pressure Due to a Column of Liquid

P = ρgh

Symbol	Quantity	Unit
P	Pressure	Pascals (Pa)
ρ	Density of the liquid	kg/m³
g	Gravitational field strength	N/kg
h	Height (depth) of the liquid column	Metres (m)

When to use it: Calculating pressure at a depth in a liquid (e.g. at the bottom of a swimming pool or in the ocean).

Worked example: Calculate the pressure at a depth of 5 m in water. (ρ = 1000 kg/m³, g = 9.8 N/kg)

P = ρgh = 1000 × 9.8 × 5 = 49,000 Pa (49 kPa)

---

Transformers

Transformer Voltage Equation

V_p / V_s = N_p / N_s

Symbol	Quantity	Unit
V_p	Primary voltage	Volts (V)
V_s	Secondary voltage	Volts (V)
N_p	Number of turns on primary coil	(no unit)
N_s	Number of turns on secondary coil	(no unit)

When to use it: Calculating unknown voltage or number of turns in a transformer.