O-Level E-Math and SEC G3 Mathematics K310
N4: Rate and speed
Connect units, average rate, speed, distance, and time while checking whether a rate is constant or changing.
Core notes
A rate compares quantities with different units. Average speed is total distance divided by total time, so unequal stages must be combined through totals rather than by averaging their speeds directly.
Average rate and average speed
Average rate is total change divided by total time or another total input. Average speed uses total distance, not displacement. When stages take different times, the arithmetic mean of the stage speeds is generally wrong.
Unit conversion
Use and . Therefore multiply kilometres per hour by to obtain metres per second, and multiply metres per second by for the reverse conversion.
Formulae and methods
| Relationship | Use |
|---|---|
| Combine all journey stages. | |
| Convert kilometres per hour to metres per second. |
Worked examples
Example 1: A runner covers in , rests for , then covers in . Find the average speed for the whole interval.
- Total distance is .
- Total time includes rest: .
- Calculate .
Answer: The average speed is to three significant figures.
Example 2: Convert to metres per second.
- Multiply by .
- Simplify the factor to .
- Calculate .
Answer: .
Chapter checkpoint
- Write both quantities and their units before dividing.
- For a multi-stage journey, total the distance and time separately.
- Convert units using a chain of equalities and check whether the answer needs an average rate or an instantaneous reading.
Exam traps and retrieval check
Avoid these traps
- Averaging stage speeds without accounting for the time spent at each speed.
- Excluding a rest period when the question asks about the entire interval.
- Converting only the numerator unit and forgetting the time unit.
Check from memory
What totals are needed for average speed?
Total distance and total time.
What converts kilometres per hour to metres per second?
Multiply by .
Does rest time affect average speed over the whole journey?
Yes, it increases total time while adding no distance.
Official K310 coverage
This chapter maps to 2 official outcomes: N4.1, N4.2. Check the official 2027 K310 syllabus for exact assessable wording and paper details.