Learning objectives
- I can explain and apply: Position and displacement.
- I can explain and apply: Constant acceleration.
- I can explain and apply: Position and velocity graphs.
Greek Lyceum Grade 1 / Physics / Two-unit revision pilot
Motion in a straight line
Motion in a straight line: structured theory, worked examples, answered practice, and a mastery checklist for Greek Lyceum Grade 1.
CHAPTER PLAN
Learn, practise, and check your progress
Follow the steps in order or jump directly to the part you need.
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completed
Estimated active study time
156 minutes
1. Understand
Objectives, key ideas, and structured theory.
Open →2. Follow the method
Worked examples that explain every step.
Open →3. Practise
Graded tasks with hints and answer guidance.
Open →4. Consolidate
Assignments from core work to challenge.
Open →5. Check
A timed, marked test with solution guidance.
Open →
Progress is stored only in this browser and does not require AI credits.
Key ideas and checks
- Average velocity = Δx/Δt.
- 1 m/s=3.6 km/h.
- A horizontal x–t graph means rest.
Unit
Core theory
The essential chapter ideas in a clear sequence before practice.
Understanding the concept
Choose an origin, positive direction and time origin. Position x may be negative. Displacement Δx=xfinal−xinitial has a sign; distance is total path length and is non-negative.
Method and conditions
For constant acceleration, v=v0+at and Δx=v0t+½at². Acceleration describes change in velocity, not velocity itself. Slowing down means opposite velocity and acceleration signs until stopping.
Checking and coverage boundaries
On an x–t graph, slope gives velocity. On a v–t graph, slope gives acceleration and signed area gives displacement. Before using a formula, check that acceleration is constant over the interval.
Original pilot material — human educator review pending
Written specifically for YourFavTeacher with AI assistance, without copying past-paper prompts. Technical and numerical checks do not replace review by a human educator. It is not an official paper or endorsed by an examination body.
Physics
Worked examples
Follow the method step by step and check why every step is valid.
Worked example 1
A body moves from x=6 m to x=21 m in 5 s. Find average velocity.
- 1Use displacement, not final position: vavg=Δx/Δt.
- 2Δx=21−6=15 m; υμ=15/5=3 m/s
- 3Keep SI units and check the sign.
3 m/s
Worked example 2
On a v–t graph, velocity rises linearly from 0 to 10 m/s in 5 s. Find displacement from area.
- 1The region under the graph is a triangle.
- 2Δx=(5·10)/2=25 m
- 3The units (m/s)·s give m.
25 m
Worked example 3
In uniform rectilinear motion, x₀=−6 m and v=5 m/s. Find x at 3 s.
- 1Do not omit the initial position.
- 2x=x₀+υt=−6+3·5=9 m
- 3Displacement is 15 m, different from final position.
9 m
Motion in a straight line
Practice with answers
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Core fluency6 minutes
A body moves from x=3 m to x=9 m in 2 s. Find average velocity.
Hint
Use displacement, not final position: vavg=Δx/Δt.
Answer guide
Use displacement, not final position: vavg=Δx/Δt. Δx=9−3=6 m; υμ=6/2=3 m/s Keep SI units and check the sign. 3 m/s
Core fluency6 minutes
A body starts from rest with constant acceleration 2 m/s² for 2 s. Find velocity and displacement.
Hint
Use v=v₀+at and Δx=v₀t+at²/2.
Answer guide
Use v=v₀+at and Δx=v₀t+at²/2. υ=2·2=4 m/s; Δx=2·2²/2=4 m Acceleration is assumed constant throughout. υ=4 m/s; Δx=4 m
Core fluency6 minutes
A body has v₀=6 m/s and acceleration −2 m/s² until it stops. Find stopping time.
Hint
Velocity is zero at the stopping instant.
Answer guide
Velocity is zero at the stopping instant. 0=6−2t ⇒ t=3 s Do not extend the equation beyond the stop without a new model. 3 s
Application6 minutes
Walk 3 m rightwards and then 2 m leftwards. Find distance and displacement.
Hint
Distance adds lengths; displacement retains signs.
Answer guide
Distance adds lengths; displacement retains signs. s=3+2=5 m; Δx=3−2=1 m Distance is not less than the magnitude of displacement. s=5 m; Δx=1 m →
Application6 minutes
On a v–t graph, velocity rises linearly from 0 to 4 m/s in 2 s. Find displacement from area.
Hint
The region under the graph is a triangle.
Answer guide
The region under the graph is a triangle. Δx=(2·4)/2=4 m The units (m/s)·s give m. 4 m
Application6 minutes
Convert 36 km/h to m/s.
Hint
Use 1 km=1000 m and 1 h=3600 s.
Answer guide
Use 1 km=1000 m and 1 h=3600 s. 36·1000/3600=10 m/s Check by multiplying by 3.6 for the inverse conversion. 10 m/s
Reasoning6 minutes
A position–time graph is horizontal. Is position or velocity zero?
Hint
Position is constant, but need not be zero.
Answer guide
Position is constant, but need not be zero. Δx=0 ⇒ υ=Δx/Δt=0 Velocity comes from the slope, not the height of the line. Zero velocity; any constant position.
Reasoning6 minutes
In uniform rectilinear motion, x₀=−3 m and v=2 m/s. Find x at 3 s.
Hint
Do not omit the initial position.
Answer guide
Do not omit the initial position. x=x₀+υt=−3+3·2=3 m Displacement is 6 m, different from final position. 3 m
Common mistakes
- Confusing distance with displacement.
- Using x instead of Δx in a displacement formula.
- Extending a slowing-down model beyond stopping without checking its validity.
Mastery check
- I can solve independently and check: Position and displacement.
- I can solve independently and check: Constant acceleration.
- I can solve independently and check: Position and velocity graphs.
Motion in a straight line
Chapter homework
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Core8 minutes
A body moves from x=4 m to x=13 m in 3 s. Find average velocity.
Hint
Use displacement, not final position: vavg=Δx/Δt.
Answer guide
Use displacement, not final position: vavg=Δx/Δt. Δx=13−4=9 m; υμ=9/3=3 m/s Keep SI units and check the sign. 3 m/s
Core8 minutes
A body starts from rest with constant acceleration 2 m/s² for 3 s. Find velocity and displacement.
Hint
Use v=v₀+at and Δx=v₀t+at²/2.
Answer guide
Use v=v₀+at and Δx=v₀t+at²/2. υ=2·3=6 m/s; Δx=2·3²/2=9 m Acceleration is assumed constant throughout. υ=6 m/s; Δx=9 m
Stretch8 minutes
A body has v₀=8 m/s and acceleration −2 m/s² until it stops. Find stopping time.
Hint
Velocity is zero at the stopping instant.
Answer guide
Velocity is zero at the stopping instant. 0=8−2t ⇒ t=4 s Do not extend the equation beyond the stop without a new model. 4 s
Stretch8 minutes
Walk 4 m rightwards and then 3 m leftwards. Find distance and displacement.
Hint
Distance adds lengths; displacement retains signs.
Answer guide
Distance adds lengths; displacement retains signs. s=4+3=7 m; Δx=4−3=1 m Distance is not less than the magnitude of displacement. s=7 m; Δx=1 m →
Challenge8 minutes
On a v–t graph, velocity rises linearly from 0 to 6 m/s in 3 s. Find displacement from area.
Hint
The region under the graph is a triangle.
Answer guide
The region under the graph is a triangle. Δx=(3·6)/2=9 m The units (m/s)·s give m. 9 m
Challenge8 minutes
Convert 54 km/h to m/s.
Hint
Use 1 km=1000 m and 1 h=3600 s.
Answer guide
Use 1 km=1000 m and 1 h=3600 s. 54·1000/3600=15 m/s Check by multiplying by 3.6 for the inverse conversion. 15 m/s
45 minutes / 40 marks
Full chapter test
A timed, full-mark self-assessment with model-answer guidance.
Show working, units and a final check. Equivalent correct methods are accepted. Timing is a revision guide, not official examination conditions.
1. A body moves from x=5 m to x=17 m in 4 s. Find average velocity.
5 marksAnswer guide
Use displacement, not final position: vavg=Δx/Δt. Δx=17−5=12 m; υμ=12/4=3 m/s Keep SI units and check the sign. 3 m/s
2. A body starts from rest with constant acceleration 2 m/s² for 4 s. Find velocity and displacement.
5 marksAnswer guide
Use v=v₀+at and Δx=v₀t+at²/2. υ=2·4=8 m/s; Δx=2·4²/2=16 m Acceleration is assumed constant throughout. υ=8 m/s; Δx=16 m
3. A body has v₀=10 m/s and acceleration −2 m/s² until it stops. Find stopping time.
5 marksAnswer guide
Velocity is zero at the stopping instant. 0=10−2t ⇒ t=5 s Do not extend the equation beyond the stop without a new model. 5 s
4. Walk 5 m rightwards and then 4 m leftwards. Find distance and displacement.
5 marksAnswer guide
Distance adds lengths; displacement retains signs. s=5+4=9 m; Δx=5−4=1 m Distance is not less than the magnitude of displacement. s=9 m; Δx=1 m →
5. On a v–t graph, velocity rises linearly from 0 to 8 m/s in 4 s. Find displacement from area.
5 marksAnswer guide
The region under the graph is a triangle. Δx=(4·8)/2=16 m The units (m/s)·s give m. 16 m
6. Convert 72 km/h to m/s.
5 marksAnswer guide
Use 1 km=1000 m and 1 h=3600 s. 72·1000/3600=20 m/s Check by multiplying by 3.6 for the inverse conversion. 20 m/s
7. A position–time graph is horizontal. Is position or velocity zero?
5 marksAnswer guide
Position is constant, but need not be zero. Δx=0 ⇒ υ=Δx/Δt=0 Velocity comes from the slope, not the height of the line. Zero velocity; any constant position.
8. In uniform rectilinear motion, x₀=−5 m and v=4 m/s. Find x at 3 s.
5 marksAnswer guide
Do not omit the initial position. x=x₀+υt=−5+3·4=7 m Displacement is 12 m, different from final position. 7 m
Unit
Official sources and verification
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Physics
Learn force diagrams, axis choice, units, and the transition from physical picture to equation.
What this chapter covers
The structure follows the official textbook layout and is used to organise study.
Position and displacement
Constant acceleration
Position and velocity graphs
Where to focus
The areas that usually create mistakes or need extra revision.
I can solve independently and check: Position and displacement.
I can solve independently and check: Constant acceleration.
I can solve independently and check: Position and velocity graphs.
Sources, daily material, and resources
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Start from the official textbook or specification referenced on the subject page.
Use the notes and examples as support, not as a replacement for the official syllabus.
Check the current syllabus version before exam preparation.
Practice by subtopic
Targeted practice before full tests so coverage is clear.
A body moves from x=3 m to x=9 m in 2 s. Find average velocity.
A body starts from rest with constant acceleration 2 m/s² for 2 s. Find velocity and displacement.
A body has v₀=6 m/s and acceleration −2 m/s² until it stops. Find stopping time.
Walk 3 m rightwards and then 2 m leftwards. Find distance and displacement.
On a v–t graph, velocity rises linearly from 0 to 4 m/s in 2 s. Find displacement from area.
Convert 36 km/h to m/s.
A position–time graph is horizontal. Is position or velocity zero?
In uniform rectilinear motion, x₀=−3 m and v=2 m/s. Find x at 3 s.
Mocks and progress checks
How to measure progress in this chapter and when it enters a cumulative mock.
Start with untimed practice by subtopic.
Move to a short timed checkpoint only after completing the mastery checklist.
Record each error with the correct method and revisit it after 48 hours.
Next step
What to do after finishing the chapter and how it connects to the next unit.
Complete the practice without support.
Explain the core method aloud in under two minutes.
Continue to the next chapter or request targeted tutor support.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.