What you'll learn
This topic covers how forces affect motion, from calculating speed and acceleration to understanding momentum and Newton's laws. You'll learn to analyse motion using graphs, apply key equations, and understand concepts like inertia, stopping distances, and safety features. These principles are essential for understanding everything from road safety to space travel.
Key terms and definitions
Scalar quantity — a quantity with magnitude only (e.g. speed, distance, mass, time)
Vector quantity — a quantity with both magnitude and direction (e.g. velocity, displacement, force, acceleration, momentum)
Resultant force — the single force that has the same effect as all the original forces acting on an object combined
Inertia — the tendency of an object to remain at rest or continue moving at constant velocity unless acted upon by a resultant force
Momentum — the product of an object's mass and velocity (measured in kg m/s)
Newton (N) — the unit of force; one newton is the force needed to give a 1 kg mass an acceleration of 1 m/s²
Terminal velocity — the constant maximum velocity reached by a falling object when the drag force equals the weight
Stopping distance — the total distance a vehicle travels from when the driver first sees a hazard until the vehicle stops (thinking distance + braking distance)
Core concepts
Distance, displacement, speed and velocity
Distance is a scalar quantity measuring how far an object has travelled, regardless of direction. Displacement is a vector quantity measuring the straight-line distance from start to finish, including direction.
Speed is distance travelled per unit time:
- speed (m/s) = distance (m) ÷ time (s)
- Average speed = total distance ÷ total time
Velocity is displacement per unit time, including direction. An object moving in a circle at constant speed has changing velocity because its direction constantly changes.
Typical speeds:
- Walking: 1.5 m/s
- Running: 3 m/s
- Cycling: 6 m/s
- Car (urban): 13 m/s
- Car (motorway): 30 m/s
- Train: 50 m/s
- Aircraft: 250 m/s
- Sound in air: 330 m/s
Acceleration
Acceleration is the rate of change of velocity:
- acceleration (m/s²) = change in velocity (m/s) ÷ time (s)
- a = (v - u) ÷ t
where u = initial velocity, v = final velocity, t = time
Deceleration is negative acceleration (slowing down). An object changes velocity when its speed changes, direction changes, or both change.
Uniform acceleration occurs when velocity changes at a constant rate. For uniformly accelerated motion:
- (final velocity)² - (initial velocity)² = 2 × acceleration × distance
- v² - u² = 2as
Distance-time and velocity-time graphs
Distance-time graphs:
- Gradient = speed
- Horizontal line = stationary
- Straight diagonal line = constant speed
- Steeper gradient = faster speed
- Curved line = accelerating (increasing gradient) or decelerating (decreasing gradient)
Velocity-time graphs:
- Gradient = acceleration
- Horizontal line = constant velocity
- Positive gradient = acceleration
- Negative gradient = deceleration
- Area under graph = distance travelled
- Curved line = non-uniform acceleration
Newton's laws of motion
Newton's First Law (Inertia): An object remains at rest or continues moving at constant velocity unless acted upon by a resultant force. This explains why passengers lurch forward when a bus brakes suddenly—their inertia keeps them moving.
Newton's Second Law:
- Force (N) = mass (kg) × acceleration (m/s²)
- F = ma
A resultant force causes acceleration. Larger mass requires larger force for the same acceleration. This is why loaded vehicles accelerate more slowly than empty ones with the same engine force.
Newton's Third Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. These forces:
- Are equal in magnitude
- Act in opposite directions
- Act on different objects
- Are the same type of force
Example: A book on a table experiences weight (gravity pulling down) and a reaction force (table pushing up). These are NOT Newton's Third Law pairs because they act on the same object. The Third Law pair to the book's weight is the gravitational pull of the book on the Earth.
Momentum and collisions
Momentum = mass × velocity
- p = mv
- Units: kg m/s
The principle of conservation of momentum states that in a closed system, total momentum before a collision equals total momentum after:
- total momentum before = total momentum after
- m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
This applies to:
- Explosions (objects starting together, moving apart)
- Collisions (objects moving together or bouncing apart)
- Recoil (e.g., gun firing a bullet)
Change in momentum = resultant force × time
- Δp = FΔt or F = Δp/Δt
Increasing collision time reduces force (same momentum change). This principle explains safety features:
- Crumple zones extend collision time
- Airbags extend time to stop passenger
- Seat belts stretch slightly to increase stopping time
- Crash mats increase time for gymnasts landing
Forces and motion
Weight is the force of gravity acting on an object:
- weight (N) = mass (kg) × gravitational field strength (N/kg)
- W = mg
- On Earth, g ≈ 10 N/kg (or 9.8 N/kg for accurate calculations)
Weight is a vector (acts downward); mass is a scalar.
Friction opposes motion between surfaces. Air resistance (drag) opposes motion through air. Both:
- Increase with speed
- Convert kinetic energy to heat
- Depend on surface area and shape
Terminal velocity occurs when drag force equals driving force (weight for falling objects). For a skydiver:
- Initially: weight > air resistance → accelerates downward
- As speed increases: air resistance increases
- Eventually: weight = air resistance → terminal velocity reached
- Parachute opens: air resistance > weight → decelerates
- New terminal velocity: lower speed when forces balance again
Stopping distances
Thinking distance = distance travelled during reaction time
- Increases with: speed, tiredness, alcohol/drugs, distractions
Braking distance = distance travelled while braking
- Increases with: speed (proportional to kinetic energy, so v² relationship), poor brakes, poor tyres, poor road conditions (wet, icy), mass of vehicle
Stopping distance = thinking distance + braking distance
At 30 mph (13 m/s): thinking ~9 m + braking ~14 m = 23 m total At 60 mph (27 m/s): thinking ~18 m + braking ~55 m = 73 m total
Note: braking distance increases dramatically with speed because kinetic energy ∝ v².
Circular motion and centripetal force
An object moving in a circle at constant speed is accelerating because velocity (a vector) constantly changes direction. This requires a centripetal force directed toward the centre of the circle.
Examples:
- Planets orbiting the Sun (gravity provides centripetal force)
- Car turning a corner (friction provides centripetal force)
- Satellite orbiting Earth (gravity provides centripetal force)
- Swing ride at a fairground (tension provides centripetal force)
Higher speed or tighter circle requires greater centripetal force.
Worked examples
Example 1: Calculating acceleration
Question: A car accelerates from rest to 25 m/s in 8.0 seconds. Calculate the acceleration of the car. (3 marks)
Solution:
- u = 0 m/s (from rest)
- v = 25 m/s
- t = 8.0 s
- a = (v - u) ÷ t (1 mark for correct equation)
- a = (25 - 0) ÷ 8.0 (1 mark for substitution)
- a = 3.125 m/s² or 3.1 m/s² (1 mark for answer with unit)
Example 2: Conservation of momentum
Question: A 1200 kg car travelling at 15 m/s collides with a stationary 800 kg car. After the collision, both cars move together. Calculate their velocity immediately after collision. (4 marks)
Solution: Total momentum before = total momentum after (1 mark for principle)
Before collision:
- Momentum = (1200 × 15) + (800 × 0) = 18,000 kg m/s (1 mark for calculation)
After collision:
- Combined mass = 1200 + 800 = 2000 kg
- 18,000 = 2000 × v (1 mark for equation)
- v = 18,000 ÷ 2000 = 9 m/s (1 mark for answer with unit)
Example 3: Forces and acceleration
Question: A resultant force of 6000 N acts on a car of mass 1500 kg. Calculate the acceleration. If the car was initially travelling at 12 m/s, calculate its velocity after 4.0 seconds. (5 marks)
Solution: Part 1:
- F = ma, so a = F ÷ m (1 mark for rearrangement)
- a = 6000 ÷ 1500 = 4 m/s² (1 mark for answer)
Part 2:
- a = (v - u) ÷ t (1 mark for equation)
- 4 = (v - 12) ÷ 4.0
- 16 = v - 12 (1 mark for rearrangement)
- v = 28 m/s (1 mark for answer)
Common mistakes and how to avoid them
Confusing distance with displacement — Remember displacement is the straight-line distance from start to finish with direction, while distance is the total path travelled. An athlete running one lap of a 400 m track travels 400 m distance but has zero displacement.
Mixing up speed and velocity — Speed is scalar (magnitude only); velocity is vector (magnitude and direction). An object can have constant speed but changing velocity if direction changes (circular motion).
Forgetting direction in momentum calculations — Momentum is a vector. Assign positive and negative directions consistently. Objects moving in opposite directions have opposite signs.
Misidentifying Newton's Third Law pairs — The paired forces must act on different objects and be the same type of force. Weight and normal reaction force on a book resting on a table are NOT Third Law pairs—they act on the same object.
Incorrect units in calculations — Always convert to standard units: metres (not cm or km), seconds (not minutes), kilograms (not grams). Check your final answer has appropriate units.
Assuming braking distance is proportional to speed — Braking distance is proportional to kinetic energy (½mv²), so it increases with speed squared, not speed. Doubling speed roughly quadruples braking distance.
Exam technique for "P2: Forces"
Command words matter: "State" requires a brief answer; "Describe" needs more detail about what happens; "Explain" requires reasons using physics principles; "Calculate" requires working, substitution into equations, and units.
Show all working in calculations — Even if your final answer is incorrect, you can earn method marks for correct equation selection, rearrangement, and substitution. Always include units with numerical answers.
Use vector diagrams carefully — When dealing with forces or momentum, draw clear diagrams showing direction with arrows. Label all forces and use a consistent scale if drawing to scale.
Link physics to real contexts — Questions often use real scenarios (cars, sports, safety features). Apply physics principles to explain observations, linking cause and effect clearly.
Quick revision summary
Forces cause changes in motion. Speed is distance per time; velocity includes direction. Acceleration is change in velocity per time. Newton's laws explain motion: objects maintain velocity unless a resultant force acts (First Law); F = ma (Second Law); forces occur in equal-opposite pairs on different objects (Third Law). Momentum (mass × velocity) is conserved in collisions. Stopping distance increases with speed, combining thinking and braking distance. Safety features reduce force by increasing collision time. Circular motion requires centripetal force toward the centre.