Forces & Motion — Complete Summary

Edexcel IGCSE Physics (4PH1) · Topic 1 · All spec points covered

Topic 1

SciMathsHub

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Key Equations

Average Speed

v = d / t

v(m/s) · d(m) · t(s)

Acceleration

a = (v − u) / t

a(m/s²) · v,u(m/s) · t(s)

Without time

v² = u² + 2as

v,u(m/s) · a(m/s²) · s(m)

Newton's 2nd Law

F = ma

F(N) · m(kg) · a(m/s²)

Weight

W = mg (g = 10 N/kg)

W(N) · m(kg) · g = 10 N/kg

Momentum

p = mv

p(kg m/s) · m(kg) · v(m/s)

Impulse

F × t = m(v − u)

F(N) · t(s) · change in p(kg m/s)

Hooke's Law

F = ke

F(N) · k(N/m) · e(m)

Pressure

P = F / A

P(Pa = N/m²) · F(N) · A(m²)

Density

ρ = m / V

ρ(kg/m³) · m(kg) · V(m³)

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Distance – Time Graphs

Gradient = speed | Curve = changing speed

Stationary

Const. speed

Accelerating

Decelerating

Reading d-t graphs

Gradient = speed | Horizontal = stationary
For a curve: draw a tangent → gradient = instantaneous speed

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Velocity – Time Graphs

Gradient = acceleration | Area = distance

Const. velocity

Const. accel.

Decelerating

Full journey

Reading v-t graphs

Gradient = acceleration | Area under graph = distance
Negative gradient = deceleration (a is negative)

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Newton's Laws

First Law

An object stays at rest or moves at constant velocity unless acted on by a resultant force.

Second Law

Resultant force = mass × acceleration
F ∝ a (double force → double acceleration)
a ∝ 1/m (double mass → half acceleration)

F = ma

Third Law

For every action there is an equal and opposite reaction. Forces act on different objects — they cannot cancel each other.

Weight vs Mass: Mass is constant (kg). Weight = mg depends on g — varies with location.

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Momentum

Momentum (vector)

p = mv

p(kg m/s) · m(kg) · v(m/s)

Conservation

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Total momentum is conserved in all collisions

Impulse = change in momentum

F × t = m(v − u)

Elastic vs Inelastic

Elastic: momentum AND kinetic energy conserved
Inelastic: momentum conserved only — KE is lost as heat/sound

Airbags / crumple zones: increase contact time → reduce force (same Δp, larger t → smaller F)

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Hooke's Law & Pressure

Hooke's Law (up to limit of proportionality)

F = ke

k = spring constant (N/m) · e = extension (m)

Elastic limit: beyond this, spring does not return to natural length (permanent deformation)
Limit of proportionality: where the graph first curves — F no longer proportional to e

Pressure

P = F / A

P(Pa = N/m²) · F(N) · A(m²)

Density

ρ = m / V

ρ(kg/m³) · m(kg) · V(m³)

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Key Definitions

Distance

Total path length — scalar (m)

Displacement

Straight-line distance + direction — vector (m)

Speed

Distance per unit time — scalar (m/s)

Velocity

Speed in a given direction — vector (m/s)

Acceleration

Rate of change of velocity (m/s²) — vector

Resultant force

Single force equivalent to all forces combined

Inertia

Tendency to resist change in motion (Newton's 1st)

Terminal velocity

Constant speed when driving force = drag force

Momentum

p = mv — vector quantity (kg m/s)

Impulse

Force × time = change in momentum

Spring constant k

Gradient of F-e graph — stiffness measure (N/m)

Extension

e = new length − natural length (m)

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Stopping Distance & Exam Tips

      stopping distance = thinking distance + braking distance
    

↑ Thinking distance

Higher speed
Tiredness / fatigue
Alcohol or drugs
Distractions

↑ Braking distance

Higher speed (most significant)
Wet or icy roads
Worn tyres or brakes
Heavier vehicle load

⚡ Common exam mistakes

D-T gradient ≠ acceleration. Gradient of d-t graph = speed, not acceleration. Acceleration needs a v-t graph.
Area under d-t graph ≠ distance. Only the area under a v-t graph equals distance.
Weight ≠ mass. Weight is a force in Newtons. Mass is in kg and does not change.
Newton's 3rd Law pairs act on different objects — they cannot cancel. "The road pushes up on the car; the car pushes down on the road."
Limit of proportionality ≠ elastic limit. Proportionality limit is where graph curves; elastic limit is where permanent deformation starts.
Momentum is conserved in ALL collisions — elastic and inelastic. Kinetic energy is only conserved in elastic collisions.