CLASS 9 SCIENCE · CHAPTER 4 · STUDY NOTES
Describing Motion Around Us
Understand describing motion around us through short explanations, labelled models and original practice. Read one topic, explain it in your own words, then check.
EXPLORE
Motion depends on the reference point
Choose an origin and a positive direction first.Track position against one fixed origin
- Position
- Location measured relative to a chosen reference.
- Motion / rest
- Position changes / stays unchanged with time relative to that reference.
A seated passenger is at rest relative to a train seat but moving relative to the platform. Neither statement is contradictory.
For one-dimensional motion, positive and negative signs show the chosen direction. Keep the origin and positive direction fixed throughout a calculation. An instant is one clock reading; an interval is the difference between two readings.
Take a moment. What do you think?
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Question
Can an object be both at rest and moving in different descriptions?
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The path length is not the net change
Add the journey for distance; subtract endpoints for displacement.Separate the two legs from the endpoint change
- Distance travelled
- Total path length covered; nonnegative.
- Displacement
- Final position minus initial position, including direction; unit metre.
In an original walk, go from 0 to 6 m, then back to 2 m. Distance = 6 + 4 = 10 m; displacement = 2−0 = +2 m.
After returning to the start, displacement is zero although distance is not. The displacement magnitude never exceeds the path length. A straight one-direction journey makes them equal.
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Question
For that walk, why is displacement not 10 m?
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Use the correct numerator
Both rates use the whole elapsed time.A return leg reduces net displacement
Position (m)
Time (s)
- Position · A one-dimensional model.
Assumptions: Original walk: position rises to 6 m, then falls to 2 m. Distance 10 m and displacement +2 m over 5 s.
Read the plotted values
Position
| Time (s) | Position (m) |
|---|---|
| 0 | 0 |
| 3 | 6 |
| 5 | 2 |
Original walk: position rises to 6 m, then falls to 2 m. Distance 10 m and displacement +2 m over 5 s.
- Average speed
- Total distance ÷ elapsed time.
- Average velocity
- Displacement ÷ elapsed time; direction matters.
If the 10 m walk takes 5 s, average speed = 2 m/s. Its +2 m displacement gives average velocity +0.4 m/s.
Do not average two speeds directly unless the relevant equal-time condition is met. For a full journey always divide total distance by total time, including pauses. Convert km/h to m/s by multiplying by 5/18.
The same time; different totals
Average speed = 10/5 = 2 m/s; average velocity = 2/5 = +0.4 m/sThe direction of the return is recorded through the position change, not by subtracting path lengths for distance.
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Question
Convert 36 km/h into m/s.
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A steady rate gives equal changes
A journey average differs from a rate at one instant.Equal time intervals, equal position increments
Position (m)
Time (s)
- Position · A one-dimensional model.
Assumptions: Ideal constant velocity +4 m/s, with origin position zero at t=0.
Read the plotted values
Position
| Time (s) | Position (m) |
|---|---|
| 0 | 0 |
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
| 5 | 20 |
| 6 | 24 |
| 7 | 28 |
| 8 | 32 |
Ideal constant velocity +4 m/s, with origin position zero at t=0.
- Uniform straight-line motion
- Constant velocity: equal position changes in equal time intervals with the same direction.
- Instantaneous velocity
- The velocity at a particular instant.
In a constant +4 m/s model, position increases by 4 m each second. A changing rate gives unequal changes across equal intervals.
A speedometer approximates speed at that moment, not the journey average. Direction is needed to turn that speed into a velocity.
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Question
Can the average speed be 4 m/s even if the speedometer varied?
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Acceleration measures velocity change
Its sign alone does not say faster or slower.Velocity rises at a constant rate
Velocity (m/s)
Time (s)
- Velocity · The sign indicates direction.
Assumptions: An original straight-line model: slope (15−3)/4 = +3 m/s². The change is not the same as the initial velocity.
Read the plotted values
Velocity
| Time (s) | Velocity (m/s) |
|---|---|
| 0 | 3 |
| 4 | 15 |
An original straight-line model: slope (15−3)/4 = +3 m/s². The change is not the same as the initial velocity.
- Average acceleration
- (Final velocity − initial velocity) ÷ elapsed time; unit m/s².
From +3 to +15 m/s in 4 s gives acceleration +3 m/s². From +15 to +3 m/s gives −3 m/s².
Speed increases when velocity and acceleration point in the same direction, and decreases when opposite. A negative-moving object with negative acceleration can speed up. Turning changes velocity even if speed stays fixed.
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Question
A vehicle has negative velocity and negative acceleration. Must it be slowing down?
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Choose a sign for up or down
Keep gravitational acceleration and velocity consistent.Velocity changes; gravity keeps pointing down
- Free-fall model
- Motion under gravity with other forces neglected.
Near Earth’s surface, use g ≈ 9.8 m/s² in a simple model. If upward is positive, acceleration is −g. If downward is positive, it is +g.
For an upward throw, velocity can be zero at the highest point while acceleration remains downward. Air resistance and variations in g are ignored in this elementary model.
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Question
At the highest point of an upward throw, is acceleration zero?
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A graph shows change, not the road shape
Name both axes, units and scales.Moving, waiting, moving again
Position (m)
Time (s)
- Position · A one-dimensional model.
Assumptions: Original piecewise constant-rate model. From 2 to 5 s position is fixed at 8 m, so the object is at rest.
Read the plotted values
Position
| Time (s) | Position (m) |
|---|---|
| 0 | 0 |
| 2 | 8 |
| 5 | 8 |
| 8 | 20 |
Original piecewise constant-rate model. From 2 to 5 s position is fixed at 8 m, so the object is at rest.
- Position–time graph
- Time on the horizontal axis, position on the vertical axis.
Plot each time–position pair. A straight line represents constant velocity; a horizontal line means position stays fixed. A curved line means velocity changes.
A line joining measurements assumes a suitable pattern between them. Sparse points alone cannot prove that the object moved at a constant rate throughout.
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Question
Does a steep graph mean the physical road is a steep hill?
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