Motion
Concept-first revision with scientific reasoning, everyday links, diagrams, worked examples and exam-focused practice.
Chapter Snapshot
- Motion is described relative to a reference point or frame.
- Distance is total path length; displacement is directed change from initial to final position.
- Speed is rate of distance; velocity is rate of displacement.
- Acceleration is rate of change of velocity.
- For uniform acceleration, v=u+at, s=ut+½at² and v²-u²=2as.
- Constant speed in a circle still involves acceleration because velocity direction changes.
What You Will Learn
- Distinguish distance from displacement and speed from velocity
- Calculate average speed and velocity
- Explain acceleration
- Interpret distance-time and velocity-time graphs
- Use equations of uniformly accelerated motion
- Explain uniform circular motion as accelerated motion
Why This Chapter Matters
A car moving at 60 km/h is not fully described until we know direction and reference. Motion becomes precise only when position is measured relative to something. The chapter develops that description step by step: distance becomes displacement when direction matters, speed becomes velocity when direction matters, and changing velocity becomes acceleration. Graphs and equations are simply two different languages for the same motion story.
Bridge from Earlier Learning
- Units of length and time
- Simple ratios
- Coordinate graphs
- Basic algebra
These ideas are reused and deepened in this chapter.
1. Reference and Position
2. Distance and Displacement
Distance is total path length and is always non-negative. Displacement is the directed change from initial to final position. Its magnitude cannot exceed distance and can be zero after non-zero travel. Walking 100 m east and 100 m west gives distance 200 m but displacement zero.
3. Speed and Velocity
Speed is distance per unit time. Velocity is displacement per unit time with direction. Average speed uses total distance divided by total time; average velocity uses total displacement divided by total time. An object can keep constant speed while changing velocity if its direction changes.
4. Acceleration
Acceleration measures rate of change of velocity. It can result from change in speed, direction or both. Negative acceleration is often called retardation in school problems, but the sign depends on the chosen positive direction. Always establish a sign convention before substitution.
5. Distance-Time Graphs
A distance-time graph shows how distance changes with time. Constant slope means uniform speed; a steeper line means greater speed. A horizontal segment means distance is not changing. Curved graphs indicate changing speed. The slope therefore converts a picture into a rate.
6. Velocity-Time Graphs
The slope of a velocity-time graph gives acceleration. For uniform acceleration the graph is a straight line. The area under the graph gives displacement because velocity multiplied by time has dimensions of distance. This graph also gives a geometric route to equations of motion.
7. Equations of Uniformly Accelerated Motion
When acceleration is constant, three equations connect initial velocity u, final velocity v, acceleration a, time t and displacement s. Choose the equation containing the known quantities and one required unknown. These equations should not be applied blindly to varying acceleration.
8. Uniform Circular Motion
In uniform circular motion, speed stays constant but direction changes continuously. Since velocity includes direction, velocity changes and the object is accelerated toward the centre. This is a key example showing that acceleration does not simply mean speeding up.
Compare the Ideas
Distance vs Displacement
| Feature | Distance | Displacement |
|---|---|---|
| Meaning | Total path length | Directed change in position |
| Type | Scalar | Vector |
| Can be zero after motion? | No | Yes |
| Relation | ≥ displacement magnitude | ≤ distance |
Visualise the Concept
Graphs turn motion into slope and area relationships.
Formula / Relationship Sheet
Formula / Key Relations
Speed
Scalar path rate.
Velocity
Direction matters.
Acceleration
Change in velocity per time.
First equation
Constant acceleration.
Second equation
Constant acceleration.
Third equation
Useful when time is not needed.
Worked Examples & Scientific Reasoning
u=0, a=2 m/s², t=5 s.
Velocity direction changes continuously.
Observe Like a Scientist
Exam Thinking Strategy
Define the reference and positive direction, list known variables with units, then choose the graph or equation that directly connects them.
Common Mistakes
Key Terms
Quick Revision
Quick Revision
- Motion is described relative to a reference point or frame.
- Distance is total path length; displacement is directed change from initial to final position.
- Speed is rate of distance; velocity is rate of displacement.
- Acceleration is rate of change of velocity.
- For uniform acceleration, v=u+at, s=ut+½at² and v²-u²=2as.
- Constant speed in a circle still involves acceleration because velocity direction changes.
- Revise the explanation behind each definition or formula, not only the wording.
Focused Practice
Slope of a velocity-time graph gives?
View Solution
Acceleration
A runner completes one full circular lap. What is displacement?
View Solution
Zero.
Velocity changes from 10 m/s to 22 m/s in 6 s. Find acceleration.
View Solution
2 m/s²
u=5 m/s, a=3 m/s², t=4 s. Find v.
View Solution
17 m/s
Can an object have zero velocity and non-zero acceleration at an instant?
View Solution
Yes, for example at the highest point of a vertical throw while gravity still acts.
Explain how distance-time and velocity-time graphs encode motion differently.
View Solution
Distance-time slope gives speed; velocity-time slope gives acceleration and area gives displacement.
Final Chapter Summary
Chapter Summary
- Motion is described relative to a reference point or frame.
- Distance is total path length; displacement is directed change from initial to final position.
- Speed is rate of distance; velocity is rate of displacement.
- Acceleration is rate of change of velocity.
- For uniform acceleration, v=u+at, s=ut+½at² and v²-u²=2as.
- Constant speed in a circle still involves acceleration because velocity direction changes.
- A strong answer explains the mechanism or reason, then uses the correct scientific term, relation or example.