Describing Motion Around Us
Welcome to the Motion Discovery Lab. Be the scientist: predict, move, measure and explain. A journey, a graph and a turning wheel will help you understand what motion really means.
1Is the passenger moving?
A passenger sits in a moving bus. One person says, “The passenger is resting.” Another says, “The passenger is moving.” Both can be correct! They are comparing the passenger with different reference points.
Position needs a reference
Choose an origin, such as a school gate. “12 m to the right of the gate” specifies position. On a straight line, choose a positive direction; the opposite direction is negative.
Rest and motion are relative
If position changes with time relative to the chosen reference, the object is moving. If it does not change, it is at rest relative to that reference.
🚌 Change your viewpoint
A bus moves right at 8 m/s. The passenger remains seated. Choose your reference.
Linear motion means motion along a straight line. A falling ball, a swimmer in a straight lane and a ball rolling down a straight incline can all show linear motion.
Time instant or time interval?
An instant is one clock reading, such as 3 s. An interval is the difference between readings. From 3 s to 9 s, the interval is 9 − 3 = 6 s.
2Two stories about one journey
Distance counts the whole path travelled. Displacement compares the final position with the initial position. A return journey can have a large distance but zero displacement.
| Distance | Displacement |
|---|---|
| Path length; no direction needed. | Net change in position; direction matters. |
| A scalar; never negative. | A vector; in one dimension its sign indicates direction. |
| Depends on the route. | Depends on the two end positions. |
| SI unit: metre (m). | SI unit: metre (m). |
🚶 Make your own journey
Start at the school gate, x = 0 m. Each step covers 5 m in 1 s. Right is positive.
Try three steps right and three left. Predict the distance and displacement before reading the result. The model counts completed steps and does not model the acceleration during turns.
Worked example · A trip with a turn
Meera walks 45 m east and 15 m west. Taking east as positive: distance = 45 + 15 = 60 m; displacement = 45 − 15 = +30 m, or 30 m east.
3Fast is not the whole story
Average velocity = displacement / total time
Speed tells how fast; velocity also tells direction. Both use m/s in SI. Include stops in the total journey time. A speedometer shows approximately the speed at that moment, rather than the average for the whole journey.
Uniform straight-line motion
Constant velocity: equal displacements in equal intervals, however small the intervals chosen. Both speed and direction stay unchanged.
Non-uniform motion
Velocity changes. The change may be in speed, direction or both. Constant speed around a circle is therefore not constant velocity.
🔁 Unit-conversion desk
m/s → km/h: multiply by 18/5
Why do these conversion factors work?
1 km/h = 1000 m / 3600 s = 5/18 m/s. Reverse the conversion by multiplying by 18/5, or 3.6.
Worked example · Why averaging two speeds can fail
A cyclist travels 80 m at 4 m/s and another 80 m at 8 m/s. Times are 20 s and 10 s. Average speed = 160/30 ≈ 5.33 m/s, not 6 m/s. The arithmetic mean of two speeds works when they last for equal times.
4Acceleration means changing velocity
Here u is initial velocity, v is final velocity, and Δt is the positive time interval. Acceleration has direction and its SI unit is m/s². Constant +2 m/s² means velocity increases by +2 m/s each second.
An object can move very fast with zero acceleration if its velocity is constant. It can also accelerate at constant speed if its direction changes.
⚡ Velocity-change calculator
Worked example · Slowing down
A skateboard moves right at +12 m/s and slows to +4 m/s in 4 s. Average acceleration = (4 − 12)/4 = −2 m/s². The acceleration points left, opposite to the motion.
Falling motion and the sign convention
Near Earth’s surface, neglecting air resistance, freely falling objects have approximately constant downward acceleration of magnitude 9.8 m/s². Choose downward as positive to use +9.8; choose upward as positive to use −9.8. Keep the convention unchanged throughout the problem.
5Graphs are stories, not roads
A position–time graph shows where the object is at different times. It does not draw the actual shape of the road. A curved graph can describe motion along a perfectly straight track.
| Graph | Slope | Area |
|---|---|---|
| Position–time | Velocity. A secant slope gives average velocity; tangent slope gives instantaneous velocity. | Not distance or displacement. |
| Velocity–time | Acceleration. | Signed area gives displacement; adding area magnitudes gives distance. |
| Speed–time | Rate of change of speed. | Area gives distance. |
📈 Choose a motion story
The dashed line marks the chosen time. Teal shading is positive velocity area; orange shading is negative velocity area. The axis scales stay fixed across all four stories.
Read a graph in four steps
1. Read the axis quantities and units. 2. Check the scale. 3. Compare slopes over the interval of interest. 4. For velocity–time graphs, calculate areas and keep their signs.
Two position graphs crossing means equal position at that instant, not necessarily equal velocity. Compare their slopes for velocity.
Area example · A triangle
A velocity–time line rises from 0 to 8 m/s over 4 s. Displacement = triangular area = ½ × 4 × 8 = 16 m. Acceleration = slope = 8/4 = 2 m/s².
6A toolkit for constant acceleration
These equations apply to straight-line motion with constant acceleration. In the equations, s means displacement and t is elapsed time from the initial instant.
s = ut + ½at²
v² = u² + 2as
| What is missing from the question? | Useful equation |
|---|---|
| Displacement s | v = u + at |
| Final velocity v | s = ut + ½at² |
| Time t | v² = u² + 2as |
Discover where the equations come from
For constant acceleration, a = (v − u)/t, so v = u + at. The straight velocity–time line encloses a trapezium: s = ½(u + v)t. Substituting v = u + at gives s = ut + ½at². Eliminating t gives v² = u² + 2as.
The area and displacement are signed. If velocity changes sign, total distance requires adding the magnitudes of the separate path segments.
🧮 Build a motion model
This mathematical model keeps acceleration constant, including after a reversal. A real braking vehicle usually stays stopped instead of automatically reversing.
Worked example · A trolley starts from rest
u = 0, a = +1.5 m/s², t = 4 s. Final velocity = 0 + 1.5 × 4 = +6 m/s. Displacement = ½ × 1.5 × 16 = +12 m.
7Why stopping is not instant
Before the driver presses the brake, the vehicle travels during the reaction time. Then it travels farther while braking. These are different parts of the stopping process.
Braking distance = u² / (2b)
Total stopping distance = reaction distance + braking distance
Here u is speed in m/s and b is the positive magnitude of the constant braking deceleration. The model assumes constant speed during reaction and straight-line braking to rest.
🚗 Will the model vehicle stop in time?
An idealised learning model, not a road-safety distance recommendation. Real conditions affect both reaction and braking.
Worked example · Separate the two stages
u = 12 m/s, reaction time = 0.5 s, b = 3 m/s². Reaction distance = 6 m. Braking distance = 144/6 = 24 m. Total = 30 m. Braking time = u/b = 4 s.
8Constant speed, changing velocity
In uniform circular motion, the path is circular and speed stays constant. Velocity changes because direction changes continuously. This means acceleration is not zero.
r is the radius and T is the period: the time for one complete revolution. Instantaneous velocity points along the tangent. In uniform circular motion, acceleration points toward the centre.
🎡 Turn the wheel
Teal: tangent velocity. Orange: inward acceleration. Dashed purple: displacement from the starting point. The diagram has a fixed visual radius; entered radius changes the physical quantities, not the drawing scale.
Half a revolution and a full revolution
Half a revolution: distance = πr; displacement magnitude = 2r. Full revolution: distance = 2πr; displacement = 0. Average velocity over a complete revolution is zero, but instantaneous velocity and speed are not zero.
A clock-hand experiment
Watch the tip of a clock’s minute hand. It has an approximately constant speed, yet changes direction continuously. Points farther from the centre cover a larger circumference in the same period, so their speeds are greater.
🧠 Connect the chapter
| Quantity | Meaning | SI unit |
|---|---|---|
| Distance | Total path length | m |
| Displacement | Final position − initial position | m |
| Average speed | Distance / elapsed time | m/s |
| Average velocity | Displacement / elapsed time | m/s |
| Average acceleration | Velocity change / elapsed time | m/s² |
Five misconceptions to defeat
- Moving does not always mean accelerating.
- Zero displacement does not mean zero distance.
- Negative acceleration does not always mean slowing down.
- A curved position graph need not mean a curved road.
- Constant speed does not guarantee constant velocity.
Explain it to a friend
Why does a swimmer’s round trip have zero average velocity? Why can a turning bicycle accelerate at steady speed? Why does doubling speed make braking much harder?
Use a sketch, a formula and one sentence for each explanation.
The questions in this page are original learning checks. This study book does not reproduce the textbook’s end-of-chapter question-answer section.
🏆 The 10-question Motion Challenge
One question at a time. Select an answer to reveal the explanation. Your first choice is recorded; restart to try again.
Your progress is retained while this page stays open. Reloading resets the activities.
