Describing Motion Around Us · Lesson 10 of 10
Chapter Summary and Practice
“Every formula returns for one final lap around the chapter.”
• Consolidate the language and equations of motion. • Select appropriate quantities and signs in numerical problems. • Interpret position-time and velocity-time graphs. • Apply kinematic equations under valid conditions. • Connect straight-line and circular motion. • Investigate motion through practical activities.
Motion is described by building a chain of precise ideas. A reference point establishes position. A change in position produces displacement, while the complete path gives distance. Dividing by time introduces speed and velocity. A change in velocity introduces acceleration. Graphs then make these rates visible, and equations allow motion with constant acceleration to be predicted.
| Concept | Detailed summary |
|---|---|
| Position | Distance and direction from a chosen reference point at an instant |
| Distance | Complete path length; no direction required |
| Displacement | Directed net change from initial to final position |
| Average speed | Total distance divided by total time |
| Average velocity | Displacement divided by time |
| Acceleration | Change in velocity divided by time |
| Position-time slope | Velocity |
| Velocity-time slope | Acceleration |
| Velocity-time area | Displacement |
| Uniform circular motion | Constant speed with continuously changing velocity direction |
The following relationships connect the descriptions, graphs and equations used throughout the chapter.
Distance and displacement answer different questions. Distance counts every segment of the route, while displacement ignores intermediate turns and connects only the endpoints. Consequently, displacement magnitude is never greater than distance. A round trip can have zero displacement without having zero distance.
Speed and velocity also differ. Average speed is based on distance; average velocity is based on displacement. A high speed does not imply high acceleration. Acceleration depends on how quickly velocity changes, and velocity can change because of magnitude, direction or both.
Graph meanings depend on the axes. On a position-time graph, height gives position and slope gives velocity. On a velocity-time graph, height gives velocity, slope gives acceleration and area gives displacement. A horizontal position-time line represents rest, while a horizontal velocity-time line represents constant velocity.
Signs must be interpreted through a declared positive direction. A negative acceleration may slow a positive-moving object, but it may speed up an object already moving in the negative direction. Equations work reliably only when signs, units and physical conditions are kept consistent.
These formulas should be selected only after identifying the required quantity, compatible units and the conditions of motion.
| Before solving | Question to ask |
|---|---|
| Reference | What is the origin? |
| Direction | Which direction is positive? |
| Path | Do I need distance or displacement? |
| Rate | Do I need speed, velocity or acceleration? |
| Units | Are all values in compatible units? |
| Condition | Is acceleration constant? |
| Equation | Which quantity is absent from the chosen equation? |
| Check | Is the sign, unit and size physically reasonable? |
At a Glance
• Position is stated relative to a reference point. • Distance records the path; displacement records net position change. • Speed uses distance; velocity uses displacement. • Acceleration measures velocity change. • Graph slope represents a rate of change. • Velocity-time area represents displacement. • Kinematic equations require constant acceleration. • Circular motion can be accelerated even at constant speed.
Revise, Reflect, Refine
Quiz
Which statement is a key takeaway from this lesson?
Which additional statement is also a key takeaway from this lesson?
Which further statement is also a key takeaway from this lesson?
Which another statement is also a key takeaway from this lesson?
Which final statement is also a key takeaway from this lesson?
Practice Problems
- A person walks 250 m to a shop, returns home, goes to the shop again and finally returns home. Find total distance and displacement.
- A student climbs from the ground floor to the fourth floor and descends to the second floor. Each floor is 3 m high. Find vertical distance and displacement.
- A scooter speedometer remains constant while the scooter follows a circular turn. Explain whether acceleration is possible.
- A car starts from rest and reaches 24 m s⁻¹ in 6 s. Find acceleration and displacement.
- A motorbike moving at 28 m s⁻¹ stops after 98 m. Find acceleration and stopping time.
- Explain how two objects can have equal velocities on a position-time graph even when they have different positions.
- A vehicle slows from 54 km h⁻¹ to 36 km h⁻¹ in 36 s with constant acceleration. Find displacement.
- A car accelerates from rest to 20 m s⁻¹ in 5 s, moves at that velocity for 10 s and stops uniformly in 6 s. Find total distance.
- A bus at 36 km h⁻¹ sees an obstacle 30 m ahead, reacts for 0.5 s and brakes at 2.5 m s⁻². Decide whether it stops in time.
- Explain whether an object fixed on the Earth can be described as at rest while the Earth moves around the Sun.
- Use a velocity-time graph to find displacement during a constant-velocity interval and during a decreasing-velocity interval.
- A minute hand of length 7 cm completes one and a half revolutions. Find distance, displacement, speed and average velocity when the time interval is 90 minutes.
Problem
A car accelerates from 0 to 20 m s⁻¹ in 5 s, continues at 20 m s⁻¹ for 10 s and stops in 6 s. Find total distance by graph area.
- 1.Acceleration region is a triangle: area = (½×5×20=50 m).
- 2.Constant-velocity region is a rectangle: area = (10×20=200 m).
- 3.Braking region is a triangle: area = (½×6×20=60 m).
- 4.Total displacement = (50+200+60=310 m).
- 5.The car moves in one direction, so distance travelled is also 310 m.
Problem
A minute hand of length 7 cm moves for 90 minutes. Find distance and displacement of its tip.
- 1.In 90 minutes, the hand completes (1.5) revolutions.
- 2.Distance = (1.5×2π R=1.5×2π×7=21π cm).
- 3.After one full revolution and another half, the tip is opposite its starting point.
- 4.Displacement magnitude is the diameter: (2R=14 cm).
- 5.Direction is from the starting point toward the diametrically opposite point.
The Journey Beyond
Make a cardboard disc with two rings of symbols, one near the edge and one closer to the centre. When the disc rotates, every point completes each revolution in the same time, but points farther from the centre travel a greater circumference. Their speeds are therefore greater. Observe how the outer symbols become harder to distinguish first.
A smartphone accelerometer can reveal tiny changes in motion. Compare readings while the phone rests on a floor and while it lies on an outstretched palm. The palm appears steady, yet small involuntary movements produce changing readings. Repeat measurements and keep the phone orientation consistent.
Starting from (v=u+at) and (s=ut+½at^2), derive (s=vt-½at^2) and (s=½(u+v)t). A second derivation can use the area of the trapezium below a velocity-time graph. Matching algebra with graph area strengthens the meaning of each term.
Plot the same position-time data using several scales. The physical relationship and calculated slope remain unchanged, but the visual steepness and use of space differ. Decide which scale communicates the data most clearly without hiding variation.
Discuss stopping distance with a vehicle mechanic. Consider wet roads, worn tyres, vehicle mass, night driving, fog, severe weather and reaction time. Organise the findings into reaction-related and braking-related factors, then use them to design a clear road-safety explanation.
For every numerical solution, state known values, convert units, choose a direction, select a valid relation, substitute with signs, include units and interpret the result.
• Motion becomes precise when reference, direction and time are stated. • Distance, displacement, speed, velocity and acceleration must not be interchanged. • Graphs reveal position, rates and accumulated displacement. • Kinematic equations predict constant-acceleration motion. • Circular motion shows that direction change alone produces acceleration.
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Motion in a Plane
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