Measurement of Time and Motion · Lesson 5 of 6
Uniform and Non-uniform Motion
“Recognise patterns of motion by comparing distances travelled in equal time intervals.”
• Distinguish linear motion from other paths of motion. • Identify uniform and non-uniform linear motion from speed and equal-time data. • Interpret a journey that speeds up, stays steady, and slows down. • Use a table of positions to find distances travelled during each interval. • Explain why average speed is useful for ordinary journeys.
Following Motion Along a Straight Line
A vehicle travelling along a straight road is in linear motion. Suppose a train sets out from station A, gathers speed until B, keeps a steady speed from B to C, and then slows as it approaches D. The track may be straight throughout, yet the pattern of its speed changes. A straight path alone does not tell us whether the motion is uniform.
Motion along a straight line at a constant speed. It covers equal distances in equal intervals of time.
Motion along a straight line whose speed changes. Equal time intervals need not contain equal distances.
Between B and C the train travels at an unchanging speed, so its motion there is uniform linear motion. Between A and B it speeds up, while between C and D it slows down; both are non-uniform. The words uniform and non-uniform describe the motion over a chosen interval, so name the interval when making a claim.
A car can move along a straight road while speeding up, braking, or stopping. Linear describes the path; uniform describes whether the speed stays constant.
Test Motion with Equal Time Intervals
Imagine noting each train’s position every ten minutes as it travels in one direction. The distance travelled in a particular ten-minute interval is its later position minus its earlier position. Compare those interval distances, not just the final positions. Equal distances in equal intervals are evidence of uniform motion across the recorded intervals on the straight track.
| Time | Train X position | X: distance in previous 10 min | Train Y position | Y: distance in previous 10 min |
|---|---|---|---|---|
| 10:00 | 0 km | — | 0 km | — |
| 10:10 | 20 km | 20 km | 20 km | 20 km |
| 10:20 | 40 km | 20 km | 35 km | 15 km |
| 10:30 | 60 km | 20 km | 50 km | 15 km |
| 10:40 | 80 km | 20 km | 75 km | 25 km |
| 10:50 | 100 km | 20 km | 95 km | 20 km |
| 11:00 | 120 km | 20 km | 120 km | 25 km |
Train X covers 20 km in each ten-minute interval. Train Y’s ten-minute distances vary: 20, 15, 15, 25, 20, and 25 km. Both reach 120 km after one hour, so both have the same average speed for that hour, 120 km/h. Yet X has uniform motion during the hour and Y does not. This is why a whole-journey average cannot reveal every change of pace.
Problem
An object moving in one direction along a straight track is at 12 m after 2 s and at 22 m after 4 s. How far did it move during those two seconds?
- 1.Identify the two positions: 12 m and 22 m.
- 2.Subtract the earlier position from the later position: 22 m − 12 m = 10 m.
- 3.It covered 10 m during the interval from 2 s to 4 s. Its average speed on that interval is 10 m ÷ 2 s = 5 m/s.
Problem
A cart covers 4 m, then 4 m, then 4 m in three successive one-second intervals on a straight track. Is this uniform?
- 1.The intervals have equal duration: one second each.
- 2.Compare the distances: 4 m, 4 m, and 4 m are equal.
- 3.Its observed motion is uniform over these intervals, with speed 4 m/s.
Problem
Train X covers 20 km in each of two ten-minute intervals. Train Y covers 10 km and then 30 km. Compare them.
- 1.Both trains cover 40 km in the same total time of 20 min. Their whole-journey average speeds are equal.
- 2.X covers equal distances in the equal ten-minute intervals, while Y covers unequal distances.
- 3.X is uniform over the recorded intervals; Y is non-uniform, despite their equal average speeds.
Why Real Journeys Often Change Pace
Traffic signals, turns, stops, slopes, and changes in effort make perfectly constant speed uncommon for long journeys. Uniform linear motion is a useful simple model. Real journeys are often non-uniform, which is why dividing total distance by total time is useful even when an object’s speed changes along the way.
Quiz
A car moves along a straight road but accelerates. Which description fits?
Which pattern in equal ten-minute intervals shows uniform linear motion?
An object moves in one direction along a straight track from the 5 m mark to the 25 m mark. What distance did it travel?
Two trains cover 120 km in the same hour. Must both have uniform motion?
What is true of the train from B to C when its speed is constant on a straight track?
Why is a whole-journey average speed useful in everyday travel?
Practice Problems
- A car covers 12 m, 12 m, and 12 m in three successive equal intervals on a straight road. Classify its motion and justify.
- A cyclist covers 50 m, 40 m, and 60 m in successive ten-second intervals. Is the motion uniform? Explain.
- A train is at 0, 15, 30, and 45 km at consecutive 15-minute readings. Complete a distance-per-interval table.
- Two objects cover 100 m in 20 s, but one moves steadily and the other stops briefly. Compare their average speeds and motion patterns.
- Describe the type of motion on each part of a straight journey that starts slowly, stays at a steady speed, and then brakes.
- Give three realistic causes of non-uniform motion in daily travel.
Key Takeaways
• Linear motion follows a straight path; uniform motion additionally requires constant speed. • Equal distances in equal time intervals indicate uniform linear motion. • Subtract consecutive positions to find the distance travelled during each interval. • Different motion patterns can have the same whole-journey average speed. • Most extended everyday journeys vary in speed, so average speed is often useful.