Measurement of Time and Motion · Lesson 3 of 6
Comparing Motion and Calculating Speed
“Learn to compare different journeys by finding distance travelled per unit time.”
• Explain what it means for one object to move faster than another. • Calculate speed using total distance and total time. • Use m/s and km/h with consistent distance and time units. • Read journey information from a timetable and compare speeds. • Distinguish a speedometer reading from an odometer reading.
Who Is Moving Faster?
Suppose two runners begin together on a straight track. At the same instant, the runner farther from the starting line has covered more distance in the same time and is faster over that interval. If both run the same race distance, the one who takes less time has the higher speed. These two comparisons are easy because one quantity is kept the same.
Now compare a short bicycle journey with a longer train journey. Distance alone cannot decide which is faster, and time alone cannot decide it either. We need to compare how much distance each covers in the same amount of time. That comparison is called speed.
The distance covered by an object in one unit of time. For a whole journey, divide its total distance by its total time.
A speed of 5 metres per second means the object covers 5 metres in each second if that speed is maintained. Since the SI units of distance and time are metre and second, the SI unit of speed is metre per second, written m/s. Journeys over longer distances are often described in kilometres per hour, written km/h.
| Distance measured in | Time measured in | Speed expressed in |
|---|---|---|
| metres (m) | seconds (s) | metres per second (m/s) |
| kilometres (km) | hours (h) | kilometres per hour (km/h) |
Dividing a distance in kilometres by a time in minutes gives km/min, not km/h or m/s. Convert the distance and time into the units wanted in the answer before doing the division.
Work Through Speed Calculations
Begin with the two measurements, choose the unit wanted for speed, and convert both measurements accordingly. Divide only after the units agree with that choice. The worked bicycle example shows why a unit conversion can be as important as the division itself.
Problem
A student cycles 3.6 km in 15 min. Find the average speed in m/s.
- 1.Convert the distance: 3.6 km = 3.6 × 1000 m = 3600 m.
- 2.Convert the time: 15 min = 15 × 60 s = 900 s.
- 3.Divide distance by time: 3600 m ÷ 900 s = 4 m/s. The student covered an average of 4 m per second.
Problem
Runner A travels 100 m in 20 s. Runner B travels 100 m in 25 s. Who is faster?
- 1.For A, speed = 100 m ÷ 20 s = 5 m/s.
- 2.For B, speed = 100 m ÷ 25 s = 4 m/s.
- 3.Runner A has the greater speed because the same 100 m took less time.
Problem
A cyclist covers 12 km in 30 min; a walker covers 3 km in 45 min. Compare their speeds in km/h.
- 1.Convert 30 min to 0.5 h and 45 min to 0.75 h.
- 2.Cyclist: 12 km ÷ 0.5 h = 24 km/h. Walker: 3 km ÷ 0.75 h = 4 km/h.
- 3.The cyclist is faster. Comparing their distances alone would not have shown the size of the difference fairly.
Find Speed from a Timetable
A railway timetable gives departure and arrival times. Subtract them to find the travel time between two stations, then use the distance listed for that segment. Repeat for several trains and compare their calculated speeds. Station stops and changes of pace are part of the elapsed journey time, so these results describe average speeds over the chosen segments.
| Train | Departure | Arrival | Distance | Time taken | Calculated speed |
|---|---|---|---|---|---|
| A | 10:00 | 10:30 | 30 km | 0.5 h | 60 km/h |
| B | 11:10 | 12:10 | 75 km | 1 h | 75 km/h |
| C | 14:00 | 14:20 | 20 km | 1/3 h | 60 km/h |
In this illustrative table, Train B has the largest distance covered in one hour, so it has the highest calculated speed between its two stations. For a real timetable investigation, copy the actual station times and distances first, then show the subtraction and division. The train’s category or name alone does not prove its speed on a particular segment.
Two Instruments in a Vehicle
A speedometer displays how fast a vehicle is moving at a particular moment, often in km/h. An odometer records distance travelled, often in kilometres. A speedometer number and an odometer number answer different questions. To calculate the average speed of a complete trip, use the trip’s total distance and total elapsed time.
Quiz
Two runners start together. After 10 s, one has covered more distance. What can you conclude for that interval?
A toy travels 24 m in 6 s. What is its average speed?
What unit results from distance in kilometres divided by time in hours?
A cyclist travels 3.6 km in 15 min. Which pair of values should be divided to get m/s?
Which instrument records the distance travelled by a vehicle?
Train A covers 40 km in 1 h and Train B covers 30 km in 0.5 h. Which has the higher average speed?
Practice Problems
- Two friends run 200 m in 40 s and 50 s. Calculate and compare their speeds.
- A bus covers 90 km between stations in 1.5 h. Find its average speed in km/h.
- A cyclist covers 1.2 km in 5 min. Convert both measurements and find the speed in m/s.
- A train departs at 09:15 and reaches the next station at 10:00, 45 km away. Find the elapsed time and average speed.
- Explain why covering a greater distance does not always mean moving faster.
- Describe how a speedometer and an odometer would help you investigate a car trip.
Key Takeaways
• Speed compares distance covered per unit time. • For a whole journey, speed equals total distance divided by total time. • Use m/s for metres and seconds, or km/h for kilometres and hours; convert before calculating. • A timetable provides elapsed time, while a speedometer and an odometer display different journey quantities.