Force
& Motion
A complete, independent TTO study guide: understand each idea, follow every calculation step, investigate the interactive labs and practise for your assessment — entirely offline.
Follow the five textbook sections first. The laboratories and extended investigations provide extra practice; they do not change the topics or difficulty required by the schoolbook. Select Test Preparation in the left menu to track every learning goal.
Motion – what you already know
Important knowledge from Year 2 before studying forces in Year 3.
In Year 2 you described how an object moves.
In Year 3 you learn why its motion changes.
Reaction distance, speed-time graphs and acceleration are especially important.
1Speed and conversions
km/h → m/s
Divide by 3.6
72 km/h = 20 m/s
m/s → km/h
Multiply by 3.6
12 m/s = 43.2 km/h
2Acceleration and velocity-time graphs
3Area under a speed-time graph
Reaction rectangle
Area = width × height
sreaction = v × treaction
Braking triangle
Area = ½ × width × height
sbraking = ½ × vinitial × tbraking
To find an unknown value in a braking triangle, double its area first: 2sbraking = vinitial × tbraking.
This gives the same familiar rectangle calculation as before.
4Stopping distance
If speed doubles and reaction time stays constant, reaction distance doubles (×2).If braking deceleration stays constant, braking distance increases fourfold (×4).
Types of Force
Book learning goal: Recognise the effects of forces and represent forces in a drawing.
A force is a push or pull.
It may change an object’s speed, direction or shape.
1Five types of force in the textbook
| Force | Typical example | Symbol |
|---|---|---|
| Muscle force | A person lifts a bag. | Fmuscle |
| Elastic force | A rubber band launches a stone. | Fv |
| Gravity | Earth attracts a falling apple. | Fg |
| Magnetic force | A magnet attracts iron. | Fm |
| Frictional force | A floor resists a sliding cabinet. | Ff |
p. 42
2Draw a force vector
A vector shows the point of application, the direction and the magnitude.
Use a ruler and the given force scale; do not add force arrows to different objects as if they acted on the same one.
3Gravity, mass and centre of mass
p. 44
- Name the five forces shown in Table 2.2 and give examples.
- Identify changes in speed, direction and shape.
- Draw force vectors using point of application, direction, magnitude and a force scale.
- Calculate mass or gravitational force using g = 9.8 N/kg.
- Locate the centre of mass of a simple or suspended object.
Measuring Forces
Book learning goal: Measure a force and understand the relationship between extension and elastic force.
1Read a force gauge accurately
A force gauge contains a spring that stretches under load.
Choose a suitable range and sufficiently fine precision.
The textbook compares 1 N and 10 N gauges with different graduation marks.
p. 48
2Extension is not total length
Extension u = stretched length − original length.
Measure both lengths from the same reference point.
3Hooke’s law and spring constant
4What can a graph tell you?
A directly proportional force-extension graph is a straight line through the origin.
To find C, choose a convenient clear point or two points and calculate ΔF / Δu.
For a graph of total spring length, first subtract the original length.
1 N/cm = 100 N/m.If the spring constant is in N/m, always convert centimetres to metres before substitution.
Practise with the measuring table and plotted points in the Spring Measurement Lab.
- Read a force gauge, describe its range and compare precision.
- Measure original length, stretched length and extension.
- Use Fv = C × u and rearrange it for C or u.
- Find the spring constant from a measured straight-line graph.
- Identify directly proportional quantities and convert N/cm to N/m.
- Use measurements to explain springs and trampoline behaviour.
Resultant Force
Book learning goal: Combine forces acting on an object and recognise equilibrium.
1Choose an object before drawing forces
The resultant force is the single force with the same effect as all forces acting on one object.
Forces in the same direction add; opposite forces subtract.
p. 54
2Equilibrium means zero resultant force
3Mass, weight, normal force and tension
Mass is measured in kg. Gravitational force is in N.
The normal force is exerted by a supporting surface; tension is exerted by a stretched rope.
In this textbook, weight means the force an object exerts on its support or suspension.
When it falls freely, it no longer exerts this supporting force, although gravity continues to act.
- Combine forces and draw a resultant for forces along a line.
- Explain equilibrium at rest and at constant velocity.
- Distinguish weight (book definition), gravity, mass, normal force and tension.
- Explain why freely falling objects can be weightless in this definition.
- Explain stable and unstable equilibrium and how stability changes.
Force and Acceleration
Book learning goal: Calculate force and acceleration, and explain the relationship between them.
1Newton’s second law
At constant mass, twice the resultant force gives twice the acceleration.At constant force, twice the mass gives half the acceleration.
2Include rolling resistance and air resistance
For a cyclist travelling forwards, the driving force acts forwards while rolling resistance and air resistance act backwards.The student must first draw these forces on one object, then use their resultant to calculate acceleration.The air resistance usually increases strongly as speed rises.
3The air resistance formula
Cr is the drag coefficient, ρ is air density, A is frontal area and v is speed.
The textbook uses a cyclist with Cr = 0.9 and air density 1.3 kg/m³.
The front area must be estimated.
When speed doubles while all other air-resistance factors stay the same, v² becomes four times as large and so does air resistance. A 50% increase in speed multiplies air resistance by 1.5² = 2.25.
Use the Air Resistance Lab to change all four variables and see their contributions.
4Calculate acceleration from velocity change
5Free fall and sliding resistance
If gravity is the only force, acceleration is g = 9.8 m/s², independently of mass (ignoring air resistance).Sliding resistance is another force that opposes motion; distinguish it from rolling resistance.
- Calculate acceleration from initial and final velocities.
- Calculate resultant force with F = ma and include resistive forces.
- Read air resistance from a graph or calculate it using the formula in exercise 42.
- Explain why speed changes air resistance so strongly.
- Explain acceleration during free fall.
- Identify the role of sliding and rolling resistance.
Road Safety
Book learning goal: Understand how reducing speed, increasing impact time and spreading force over area reduces the consequences of traffic accidents.
1Impact time and impact force
A collision is a change in velocity.
The same speed change in a longer time produces a smaller average force.
This is why controlled deformation matters. The central goal during a collision is to increase the stopping time. The same Δv over a longer Δt gives a smaller average deceleration and average force.
2Pressure: the area matters
To calculate pressure in N/cm², use force in newtons and contact area in cm².If you need N/m², multiply by 10,000.This is the same value as in pascals, but N/m² makes the physical meaning clearer.
3Why restraint systems matter
Crumple zone
A deformable vehicle structure can extend the vehicle’s stopping distance and time.
Seat belt
Restrains the occupant so the person stops over time rather than hitting a hard surface.
Airbag
Used with a seat belt, increases available stopping distance and contact area for some body regions.
4Connection to braking before impact
In Year 2 you learned that stopping distance is reaction distance plus braking distance.During Year 3 accident investigations, you also use this information to estimate how much speed was lost before impact.
Use the Rectangle & Triangle Lab, the Crash Investigation Lab and the Passenger & Pressure Lab for additional practice.
Real collisions involve complex acceleration, multiple contact surfaces and material properties.Our simulations calculate approximate average forces and average pressure.They cannot predict injury or diagnose a skull fracture; any thresholds used in exercises are fictional classroom comparisons.
- Explain how crumple zones, belts, airbags and helmets affect force, time and area.
- Calculate a mean impact force using a speed change and stopping time.
- Calculate pressure in N/cm², and convert to N/m² using powers of ten.
- Explain the influence of the initial speed on braking and collision outcomes.
- Solve linked collision scenarios involving a vehicle and an occupant.
Force-Vector Studio: draw first, calculate next
Three separate skills: draw the forces, calculate the resultant, then decide what the motion does.
Cart moving on a horizontal surface
See the complete six-step calculation and drawing rules
Equilibrium
Acceleration versus deceleration
Equilibrium is not the same as stability
Balanced forces explain motion.Stability explains what happens if the object is disturbed or its centre of mass moves.
Equilibrium = balanced effect
Stability = resistance to tipping
Does the line of gravity fall inside the support area?
From braking deceleration to collision force
Use the same two physics steps for ordinary braking and for a collision. A crash is simply a much larger speed change over a much shorter time.
Explore why we want to make a collision last longer
See ASKED → GIVEN → FORMULA → CONVERT → CALCULATE → ANSWER
Rectangle & Triangle Lab
Calculate reaction distance and braking distance by reading numbered axes and measuring shaded areas.
A reaction rectangle has area speed × reaction time. A braking triangle has area ½ × initial speed × braking time.
Double the triangular area first to turn it into a full rectangle: 2sbraking = vinitial × tbraking.
width = treaction; height = vinitial
base = tbraking; height = vinitial
Same reaction time and the same magnitude of braking deceleration in both cases; braking time is therefore longer at the higher speed.
Original triangle area: sbraking.
Rectangle area after doubling: 2 × sbraking.
The rectangle makes rearranging for time or speed easier.
Sometimes you know the distance and time.Other times you must work backwards.Choose any unknown, or use a random problem.
See the full six-step calculation
Spring Measurement Lab
Measure a spring, plot the force–extension relationship and find the spring constant from the gradient.
Follow the textbook: the spring constant is C = Fv / u, where u must be in metres if C is in N/m. A straight line through the origin shows direct proportionality.
The graph and data table belong to an unknown spring.Read a point, convert extension from cm to m, and calculate its spring constant.
| Extension (cm) | Elastic force (N) |
|---|
Show graph method and worked calculation
Air Resistance Lab
Investigate the drag formula from textbook exercise 42 and the square relationship between speed and resistance.
📖 p. 63 Always convert km/h to m/s before squaring the speed. A doubled speed gives four times the air resistance when other factors stay fixed.
Double the speed
The speed is ×2. The drag is ×4.
Increase speed by 50%
The speed is ×1.5. The drag is ×2.25.
It is the square of the speed ratio that matters.
Traffic Accident Investigation
Use braking marks, assumed braking deceleration, impact speed and crumple-zone deformation to reconstruct what happened.
There is no universal legally required braking deceleration.
Every exercise explicitly gives an assumed average deceleration or measured condition.
Road surface, tyres, ABS and road slope affect real stopping distances. A skid-mark calculation is only an idealised estimate, not proof by itself.
Uniform-deceleration model.Stopping time = 2 × crush distance ÷ impact speed, and average force = mass × speed² ÷ (2 × crush distance).The real force varies during deformation.
Passenger & Pressure Lab
Run a collision with no belt, with a belt, or with a belt and airbag.Compare average force, impact time and effective contact pressure.
The model calculates average pressure as average force divided by an illustrative contact area.Read it in N/cm²; the equivalent in N/m² is also shown.Real restraint forces change throughout a collision and act over different contact surfaces.This numerical model cannot predict injuries.
These values cannot tell whether a passenger will suffer a skull fracture or any other injury.Pressure alone is not a validated injury criterion, and contact conditions vary. A fictional threshold may be used in classroom questions to practise numerical comparison, but never as a medical prediction.
Formula Cards and Visual Method
Start with the picture or formula triangle, then write every step with units.
Reaction rectangle
sr = vi × tr
Spring law
Fv = C × u
Newton's second law
Fres = m × a
Pressure
p = F / A
Original area: sb = (vi × tb) / 2. Double it first: 2sb = vi × tb.
Now use the same rectangle rearrangement:
sb = ½ vi tb
vi = 2sb / tb
tb = 2sb / vi
| Quantity | Formula / relationship | Units |
|---|---|---|
| Average speed | v = s / t | m/s |
| Acceleration | a = Δv / Δt | m/s² |
| Gravity | Fg = m g | N |
| Spring force | Fv = C u | N; C in N/m, u in m |
| Resultant force | Fres = ma | N |
| Air resistance | Fair = ½ Crρ A v² | N; ρ kg/m³, A m², v m/s |
| Reaction distance | sr = v tr | m |
| Braking distance | sb = ½ v tb | m |
| Uniform braking distance | sb = v² / (2 ab) | m; ab positive magnitude |
| Impact force (average) | F = m |Δv| / Δt | N |
| Pressure | p = F / A | Pa = N/m² |
Rearranging Formulas – Learn, Try, Check
Move a symbol to the left by applying the same operation to both sides.Use the formula triangle as a memory aid, but explain the algebra as well.
To make F the subject, multiply both sides by A.
So F = p × A. Example: 12 N/cm² × 5 cm² = 60 N.
Multiply by A, then divide by p.Whatever you do to one side, do to the other.
Example: 60 N ÷ 12 N/cm² = 5 cm².
Read the starting formula, make the requested symbol the subject, and enter the new formula.
Use * to multiply and / to divide.
Rearrange the complete air-resistance formula
These exercises are more demanding than a three-variable formula triangle.Work backwards using the same operation on both sides.
Worked algebra and unit check
R questions and I questions
R = Recall / Reproduction. I = Insight / Interpretation.Practise both remembering a rule and applying it to a new situation.
Select a category or start the quiz.
Physics Flashcards
Look at the front, say your answer out loud, then flip the card to check it.Repeat the difficult cards.
Test Preparation – All Learning Goals
Tick each goal after you can explain it without looking at your notes.These are paraphrases of the textbook goals plus clearly separated practice extensions.
Year 2 revision · Motion Physics NASK HV 12 Ch.2
§2.1 · Types of Force Physics 3 VG TTO p.45
§2.2 · Measuring Forces Physics 3 VG TTO p.51
§2.3 · Resultant Force Physics 3 VG TTO p.57
§2.4 · Force and Acceleration Physics 3 VG TTO p.63
§2.5 · Road Safety Physics 3 VG TTO p.69
Extension investigations · extra practice Not additional textbook learning goals
Complete the textbook’s own Test Preparation questions on pages 72–73.Then use the extended calculations and case studies below to become confident with multi-step problems.
Practice Exam & Case Studies
A larger bank of demanding problems with numerical answers, worked solutions and individual feedback.
Write down ASKED → GIVEN → FORMULA → CONVERT UNITS → CALCULATE → ANSWER + UNIT on paper.
Enter the numerical value and select Check.
Use Show solution only after attempting the question.
Numerical tolerances allow for sensible rounding.
Linked investigations – multi-part challenges
These investigations require several calculations.They are more demanding than a single textbook question but use the same equations and graph methods.