Measurement of Time and Motion · Lesson 6 of 6
Chapter Summary and Practice
“Bring timekeeping and motion together, then apply the chapter’s ideas to mixed problems.”
• Connect repeated events, clocks, time periods, and units of time. • Choose and use the speed, distance, or time relationship in a problem. • Distinguish uniform motion from a journey that only has a stated average speed. • Interpret tables of positions and distances in equal time intervals. • Solve mixed numerical and reasoning problems with consistent units.
The Chapter in One View
We began with the need to measure intervals between events, then explored repeating processes that make clocks possible. The same measured intervals let us describe motion: distance compared with time gives speed. Finally, equal-time observations show whether a straight-line journey maintains that speed or changes it.
| Idea | What to remember | A useful check |
|---|---|---|
| Timekeeping | A repeatable or calibrated change marks an interval. | What event or change is being counted? |
| Pendulum | One oscillation is a complete back-and-forth journey; its time is the period. | Did the bob return to its starting state? |
| Time units | The SI unit is s; 60 s = 1 min and 60 min = 1 h. | Are number and unit written correctly? |
| Speed | Total distance ÷ total elapsed time gives whole-journey average speed. | Do distance and time match the requested unit? |
| Distance and time | Distance = speed × time; time = distance ÷ speed. | Does the calculated unit make sense? |
| Motion pattern | A straight path at constant speed is uniform linear motion. | Are distances equal in equal time intervals? |
Connect Timekeeping to Speed
Suppose a runner covers 100 m. Measuring only the distance cannot tell us the runner’s speed. A stopwatch supplies the interval from start to finish. Dividing 100 m by that interval produces an average speed for the race. A more precise clock can separate very close finishing times, while a consistent unit lets us compare races.
A pendulum illustrates the deeper connection: a clock needs a repeatable process to mark intervals. Its period can be estimated by timing many full oscillations and dividing by their number. A calibrated instrument then makes the time measurement used in a speed calculation more trustworthy.
Worked Mixed Examples
A mixed question may ask for a conversion before it asks for speed, or ask whether a computed average implies uniform motion. State what each number measures, keep the units visible, and check whether the question concerns one interval or an entire journey.
Problem
A horse runs at 18 m/s. A train travels at 72 km/h. Which is faster?
- 1.Convert the train speed: 72 km/h = (72 × 1000 m) ÷ (60 × 60 s).
- 2.The train speed is 20 m/s.
- 3.Compare like units: 20 m/s is greater than 18 m/s, so the train is faster by 2 m/s.
Problem
A vehicle covers 2 km in 200 s. It travels the first 500 m at 10 m/s and the next 500 m at 5 m/s. What steady speed is needed over the remaining distance?
- 1.Convert the total distance to 2000 m. The first 500 m takes 500 ÷ 10 = 50 s; the next 500 m takes 500 ÷ 5 = 100 s.
- 2.The remaining distance is 2000 − 1000 = 1000 m. The remaining time is 200 − 150 = 50 s.
- 3.Required speed = 1000 m ÷ 50 s = 20 m/s. Whole-journey average speed = 2000 m ÷ 200 s = 10 m/s.
Problem
A toy on a straight track is at 0, 5, 10, and 15 m after 0, 2, 4, and 6 s. Classify the recorded motion.
- 1.Subtract consecutive positions: 5 m, 5 m, and 5 m.
- 2.Each distance was covered in an equal two-second interval.
- 3.The recorded motion is uniform linear motion; speed = 5 m ÷ 2 s = 2.5 m/s.
Misconceptions to Check
An oscillation is a complete return, not a single trip from one extreme to the other. A speedometer gives a reading for a moment, while a journey’s average uses total distance and time. Two journeys may have the same average speed even if only one is uniform. A straight path describes the shape of a journey and does not guarantee constant speed.
A correct average speed is not evidence that the object moved uniformly. To make a uniform-motion claim, compare distances covered during equal time intervals on a straight path.
Quiz
A pendulum takes 24 s for 12 complete oscillations. What is its period?
Which measurement allows speed to be calculated from a known distance?
A car covers 180 km in 3 h. What is its average speed?
Which pair of interval distances indicates non-uniform motion over equal intervals?
A train travels 90 km at an average speed of 45 km/h. What total time is represented?
Two runners cover the same distance. Who has the higher average speed?
Practice Problems
- Describe how a sundial and a water clock mark time. State one limitation of each.
- A pendulum makes 30 oscillations in 60 s. Find the time period and explain what was counted.
- A car travels 150 m in 10 s. Find its speed in m/s, then convert it to km/h.
- Two runners each travel 400 m. One takes 50 s and the other 45 s. Calculate both speeds and their difference.
- A train travels at 25 m/s for a total distance of 360 km. Convert units and calculate its travel time.
- A train travels 180 km in 3 h. Give its average speed in km/h and m/s, then find the distance it would cover in 4 h at that steady speed.
- Compare 18 m/s with 72 km/h using the same unit.
- Explain, using a straight highway and a crowded city road, how linear journeys can be uniform or non-uniform.
- A car covers 60 km, 70 km, and 50 km in three consecutive hours. Is its motion uniform over those hours? Find the average speed.
- A straight-track object is recorded every 10 s at positions 0, 8, 16, 24, and 32 m. Find each interval distance and classify its motion.
- Another object is recorded every 10 s at positions 0, 6, 16, 21, and 35 m. Classify the motion and find its average speed over the full 40 s.
- A vehicle covers 2 km in 200 s. The first 500 m is at 10 m/s and the next 500 m at 5 m/s. Find the required speed for the remaining distance and the average for the whole journey.
- Give three everyday causes of non-uniform motion and explain why a whole-journey average remains useful.
- Plan an investigation of a playground swing that changes length while controlling the rider and measuring ten complete swings each time.
Key Takeaways
• Reliable time measurement uses a repeatable or calibrated process; a pendulum’s period is the time for one full oscillation. • The second (s) is the SI unit of time; convert minutes and hours before mixing them with seconds. • Speed connects distance and time, and the total-distance-to-total-time ratio gives a whole-journey average. • Uniform linear motion covers equal distances in equal time intervals along a straight path. • Check units, define the interval being studied, and distinguish an average from the changing motion within it.
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Uniform and Non-uniform Motion
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