2.1Representing Motion

Picturing Motion and Coordinate Systems — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 3 of 5 1 quiz

📚 American System Physics Hub / Topical Revision

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Lesson summary

Draw motion diagrams and particle models for moving objects.Displacement = final position − initial positionΔx = xf − xi (m).Time interval = final time − initial timeΔt = tf − ti (s).Collinear vectors in the same direction add3 m east + 4 m east = 7 m east.Collinear vectors in op…

Collinear vectors in opposite directions subtract
Perpendicular displacements
A vector subtraction A − B equals A + (−B)
A car is at x = −4.0 m at t = 2.0 s and x = +11.0 m at t = 5.0 s. Find Δx and Δt
Coordinate system
Frame of reference

Part 1 of 7Key ideas

Key ideas

Displacement

Displacement final position − initial position

Δx = x_f − x_i (m).

Time interval

Time interval final time − initial time

Δt = t_f − t_i (s).

Collinear vectors in the same direction add

3 m east + 4 m east = 7 m east.

Collinear vectors in opposite directions subtract

3 m east + 4 m west = 1 m west.

Perpendicular displacements

Perpendicular displacements magnitude of resultant = √(a² + b²) (Pythagoras).

In a motion diagram, equal spacing = constant speed; increasing spacing = speeding up; decreasing spacing = slowing down.

A negative position means the object is on the negative side of the origin, not that it has "less than zero" size.

Part 2 of 7Learning objectives

Draw motion diagrams and particle models for moving objects.

Set up a coordinate system and describe position with sign and unit.

Distinguish scalar from vector quantities, and distance from displacement.

Calculate displacement and time intervals and add collinear vectors.

Part 3 of 7Essential knowledge

2.1 Picturing Motion and Coordinate Syste… concept map: Displacement = final position, Time interval = final time −, Collinear vectors in the same, Collinear vectors in opposite, Perpendicular displacements — Visual guide to the key ideas explained in this lesson.

Describing motion needs a reference point; a passenger sitting in a moving train is at rest relative to the train but moving relative to the ground.

A motion diagram records positions at equal time intervals. Dots close together mean the object moves slowly; dots far apart mean it moves fast.

The particle model reduces an object to a point, ignoring size, shape and rotation. It works when the object is small compared with the distances involved.

A coordinate system needs an origin and a positive direction. Positions on the other side of the origin are negative. The choice is yours, but you must use it consistently.

Scalars have only magnitude (e.g. 20 m, 5 s). Vectors have magnitude and direction (e.g. 20 m north). Vectors are drawn as arrows whose length represents magnitude.

Distance is the total path length; displacement is the straight-line change in position. Running one full lap of a 400 m track: distance 400 m, displacement 0.

Displacement Δx = x_f − x_i. Its sign gives direction. Moving from x = +8 m to x = +2 m gives Δx = −6 m (6 m in the negative direction).

Time interval Δt = t_f − t_i; time is a scalar.

Vectors add tip-to-tail. For vectors along one line, add magnitudes if same direction, subtract if opposite; the direction is that of the larger.

For two perpendicular vectors, the resultant magnitude is found by Pythagoras and the direction by tan θ = opposite/adjacent.

12A vector subtraction A − B equals A + (−B)

A vector subtraction A − B equals A + (−B) reverse B and add it tip-to-tail.

Part 4 of 7Process & sequence

Choose an origin (e.g. the starting point) and mark it zero.

Choose which direction is positive (e.g. right or east) and draw an axis arrow.

Draw a motion diagram: dots at equal time intervals, numbered in order.

Measure the position x of the object at each time from the origin, with sign.

Find the displacement for an interval: Δx = x_f − x_i, giving magnitude and direction.

Add up path lengths to obtain distance travelled if the object changes direction.

Drawing a motion diagram and particle modelwrite these steps in this order; each step is a marking point.

Imagine photographs of the object taken at equal time intervals.

Replace each image with a single dot at the object's centre (particle model).

Number the dots 0, 1, 2 ... in time order.

Add an origin and positive-direction arrow along the path.

Compare spacing: equal = constant speed; growing = speeding up; shrinking = slowing down.

Part 5 of 7Worked examples

420 m

A runner goes 300 m east then 120 m west. Find the distance travelled and the displacement.

Distance = 300 + 120 = 420 m.
- Taking east as positive, displacement = +300 + (−120) = +180 m, i.e. 180 m east.

50 m

A student walks 30 m north then 40 m east. Find the magnitude and direction of the displacement.

Magnitude = √(30² + 40²) = √(900 + 1600) = √2500 = 50 m.
- Direction: tan θ = 40/30, θ = 53° east of north (N53°E).

+15.0 m

A car is at x = −4.0 m at t = 2.0 s and x = +11.0 m at t = 5.0 s. Find Δx and Δt.

Δx = 11.0 − (−4.0) = +15.0 m (15.0 m in positive direction). Δt = 5.0 − 2.0 = 3.0 s.

Part 6 of 7Summary

Motion is a change in position relative to a frame of reference.

The particle model treats an object as a single dot.

Distance is a scalar path length; displacement is a vector change in position.

A coordinate system sets the origin and positive direction.

Vectors add tip-to-tail; the resultant goes from first tail to last tip.

Part 7 of 7Compare: Compare

Distance vs displacement
Feature	Distance	Displacement
Type	Scalar	Vector
Depends on	Actual path taken	Only start and end positions
Can be negative?	No	Yes (sign shows direction)
Round trip back to start	Total path length	Zero
Symbol / unit	d, m	Δx, m

Scalars and vectors
Scalar	Matching vector
Distance	Displacement
Speed	Velocity
Mass	Weight (force)
Time	—

Key terms

Command terms

Identify / Describe (FRQ)

A short, specific statement; describing requires relevant characteristics, not a single word.

Explain / Justify (FRQ)

Give the cause-and-effect reasoning or evidence; a restated fact does not score.

Calculate

Show setup, substitution and the answer with units.

Predict

State the expected outcome; add a reason only if asked to justify.

MCQ technique

Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Exam technique

Keywords the mark scheme looks for in this lesson

Motion · Motion diagram · Particle model · Coordinate system · Origin · Position · Distance · Scalar · Vector · Displacement · Time interval · Resultant · Frame of reference

Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).

Use precise vocabulary, never “it/stuff/things”.

Show units and working in calculations.

In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

displacement is the distance travelleddisplacement is the change in position in a stated direction.

displacement = 50 mdisplacement = 50 m north (vectors need direction).

a vector is a big quantitya vector has both magnitude and direction.

negative displacement means it went backwards in timenegative displacement means it moved in the negative direction.

Last updated: 18 October 2026