Forces & Motion

Speed: Distance / time (scalar — no direction)

Velocity: Displacement / time (vector — has direction)

Example:
Car travels 100 m east in 5 s → speed = 20 m/s, velocity = 20 m/s east

Acceleration: Change in velocity / time

where: u = initial velocity, v = final velocity, t = time

Negative acceleration (deceleration):
Velocity decreases (e.g., braking)

Example:
Car accelerates from 0 to 20 m/s in 4 s
a = (20 - 0) / 4 = 5 m/s²

Gradient (slope) = Speed

Steep line → high speed | Flat line → stationary

Curved line: Acceleration (gradient changing)

Gradient increases → speeding up (acceleration)

Gradient decreases → slowing down (deceleration)

Gradient (slope) = Acceleration

Steep upward line → large acceleration

Flat line → constant velocity (no acceleration)

Area under curve = Distance traveled

Rectangular area: distance = v × t

Triangular area: distance = ½ × base × height

Free fall: Object falls under gravity alone (no air resistance)

Acceleration due to gravity: g ≈ 9.8 m/s² (or 10 m/s² for approximation)

Equations of motion:

v = u + at

s = ut + ½at²

v² = u² + 2as

Mass: Amount of matter (kg) — scalar, never changes

Weight: Gravitational force on mass (N) — vector, downward

where: m = mass (kg), g ≈ 9.8 m/s²

Example: 50 kg person on Earth
Weight = 50 × 9.8 = 490 N
Same person on Moon (g ≈ 1.6 m/s²) weighs only 80 N!

where: ρ = density (kg/m³), m = mass (kg), V = volume (m³)

Measuring density:

Regular solid: measure length, width, height → calculate volume

Irregular solid: water displacement method (volume of water displaced = volume of object)

Liquid: use measuring cylinder

Inertia: Resistance to change in motion

Greater mass → greater inertia → harder to accelerate

Real example:
Car brakes suddenly → passengers lurch forward (inertia keeps them moving)

where: F = net force (N), m = mass (kg), a = acceleration (m/s²)

Key insights:

• Double force → double acceleration

• Double mass → half acceleration

• Net force = all forces added together (account for directions)

Key points:

• Equal in magnitude, opposite in direction

• Act on DIFFERENT objects

• Simultaneous (happen at same time)

Example:
Person pushes wall with 100 N → wall pushes back on person with 100 N (opposite direction)

Friction: Force opposing motion between surfaces in contact

Factors affecting friction:

• Normal force (heavier object = more friction)

• Surface roughness (rougher = more friction)

• Type of surfaces (different materials have different coefficients)

Air resistance (drag): Friction from air (increases with speed)

Streamlined shapes reduce drag (cars, fish, birds)

Example: Falling object

1. Initially: weight > air resistance → accelerates downward

2. As speed increases: air resistance increases

3. Eventually: air resistance = weight → terminal velocity reached

Real example: Skydiver without parachute reaches ~53 m/s. With parachute → larger drag → slower terminal velocity (~5 m/s)

where: F = force (N), k = spring constant (N/m), x = extension (m)

Spring constant (k): Stiffness of spring

Large k → stiff spring (hard to stretch)

Small k → soft spring (easy to stretch)

Example: Spring with k = 100 N/m
Force to extend 0.05 m = 100 × 0.05 = 5 N

Unit: N·m (newton-metres)

Principle of moments (equilibrium):

Sum of clockwise moments = Sum of anticlockwise moments

Example (seesaw):
Left: 500 N at 2 m from pivot = 1000 N·m clockwise
Right: Force F at 4 m = 1000 N·m anticlockwise
F × 4 = 1000 → F = 250 N

Centre of gravity: Point where all weight acts (entire mass concentrated here)

For uniform objects: at geometric center

Stability: How resistant an object is to tipping

Example: Wide, squat object (stable) vs tall, narrow object (unstable)

where: p = momentum (kg·m/s), m = mass (kg), v = velocity (m/s)

Key property: Vector quantity (has direction)

Conservation of momentum:

Total momentum before collision = Total momentum after collision

Formula: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Impulse: Change in momentum caused by a force

where: F = force (N), Δt = time (s)

Safety features use impulse:

• Airbags: Increase Δt → reduce F (force on body)

• Crumple zones: Increase Δt → gentler deceleration

• Seatbelts: Distribute force over larger area

Kinetic energy: Energy of motion

Gravitational potential energy: Energy due to height

Conservation of energy:
Total energy at start = Total energy at end (no loss)

On frictionless slope: Eₚ lost = Eₖ gained

Work: Energy transfer when force moves object

where: W = work (J), F = force in direction of motion (N), d = distance (m)

Power: Rate of energy transfer

where: P = power (W), t = time (s)

Efficiency: Fraction of input energy converted to useful output

No machine is 100% efficient!
Energy is lost to friction, heat, sound

Example: Electric motor (80% efficiency)
Input 100 J → Output 80 J useful work + 20 J wasted as heat

Non-renewable: Limited supply, will run out

• Fossil fuels (coal, oil, gas) — pollute, contribute to climate change

• Nuclear — no CO2, but radioactive waste

Renewable: Replenish naturally, sustainable

• Solar — depends on weather

• Wind — variable, needs suitable locations

• Hydro — reliable but dams impact ecosystems

• Geothermal — limited to specific regions

✅ Speed = distance/time | Velocity = displacement/time (with direction)

✅ Acceleration = change in velocity / time

✅ Newton's 3 laws: 1st (inertia), 2nd (F=ma), 3rd (action-reaction)

✅ Weight = mg | Density = mass/volume

✅ Terminal velocity: when drag = driving force (no acceleration)

✅ Hooke's law: F = kx (spring constant)

✅ Momentum = mv | Conservation: momentum before = after

✅ Energy: Eₖ = ½mv² | Eₚ = mgh | Work = Fd | Power = W/t

✅ Efficiency = useful output / total input

Master forces & motion — unlock Topic 1! ⚡