Did you know? A speed of 10 metres per second is exactly 36 kilometres per hour, 600 metres per minute and 1000 centimetres per second. The motion is identical in all four descriptions. What changes is the unit of distance and the interval of time.
For parents seeking a Secondary 1 G2 Mathematics tutor in Bukit Timah, the practical method is separate the distance conversion from the time conversion, label each rate, and reverse the result to confirm that no factor of 60, 100 or 1000 was lost. The familiar 3.6 shortcut follows from those unit relationships.
The MOE G2 Mathematics syllabus explicitly includes speed in km/h, m/min, m/s and cm/s, plus speed-unit conversions in Secondary 1. The unchanged eduKateSG Secondary 1 small-group reference describes weekly 90-minute tutorials with three students near Sixth Avenue MRT. These travel speeds are fictional mathematical examples, not live transport timings.
Every conversion in one minute
- km/h → m/s: divide by 3.6 (equivalently ×5/18).
- m/s → km/h: multiply by 3.6.
- m/s → m/min: multiply by 60.
- m/min → m/s: divide by 60.
- m/s → cm/s: multiply by 100.
- cm/s → m/s: divide by 100.
- m/min → km/h: multiply by 0.06.
- cm/s → km/h: multiply by 0.036.
- Distance = speed × compatible duration.
- Use total distance divided by the relevant total time for average speed.
Where the conversion factor 3.6 comes from
Start with one metre per second. In one hour there are 3600 seconds, so constant motion at that rate covers 3600 metres per hour. Divide by 1000 metres per kilometre, and the rate is 3.6 kilometres per hour. Thus m/s multiplied by 3.6 gives km/h.
Reversing, 36 km/h means 36,000 metres in 3600 seconds, or ten metres per second. The result is not a trick about shifting decimal places; it is exactly the same amount of distance covered over compatible time intervals.
36 fundamental ideas about unit speed
1. Speed compares distance with duration
Speed is distance travelled per unit of time. The word per describes the denominator unit, such as kilometres per hour or metres per second. A correctly calculated numeral without matching units can answer a different question.
Worked example: If twenty metres are travelled in four seconds at constant speed, rate is 20/4=5 m/s.
Checking question: Write the distance unit above and time unit below before dividing.
2. One kilometre contains one thousand metres
Converting kilometre measurements to metres multiplies by 1000. Reverse conversion divides by 1000. This is one part of changing km/h to m/s, not the entire conversion.
Worked example: 2.4 km=2400 m.
Checking question: Check that a larger number of smaller metres represents the same distance.
3. One hour contains 3600 seconds
An hour has sixty minutes and each minute has sixty seconds. Thus 60×60=3600 seconds per hour. This is the second essential step in converting km/h to m/s.
Worked example: Half an hour is 1800 seconds; one quarter hour is 900 seconds.
Checking question: Do not divide by sixty once and call the result metres per second.
4. km/h to m/s uses 1000 divided by 3600
To turn kilometre-per-hour rate into metre-per-second, convert the distance numerator by 1000 and the time denominator by 3600. The combined factor is 1000/3600=1/3.6.
Worked example: 36 km/h=36÷3.6=10 m/s.
Checking question: The numerical speed becomes smaller because the per-second interval is shorter and metres replace kilometres.
5. m/s to km/h uses the inverse factor 3.6
Reversing km/h to m/s multiplies the metre-per-second rate by 3600/1000=3.6. Both rates describe identical physical motion.
Worked example: 10 m/s=10×3.6=36 km/h.
Checking question: Check by converting the result back to ten metres per second.
6. m/s to m/min multiplies by sixty
The distance in one minute is sixty times the distance in one second at the same constant speed. Thus m/s becomes m/min by multiplying by sixty.
Worked example: 5 m/s=300 m/min.
Checking question: In sixty seconds at five metres each, total is three hundred metres.
7. m/min to m/s divides by sixty
A metre-per-minute rate describes distance accumulated over sixty seconds. Dividing by sixty gives the corresponding distance per second.
Worked example: 300 m/min=300/60=5 m/s.
Checking question: Multiply the recovered m/s by sixty to get the original.
8. m/s to cm/s multiplies by one hundred
A metre is 100 centimetres. Both rates use the same one-second denominator, so only the distance unit changes.
Worked example: 5 m/s=500 cm/s.
Checking question: Check that the numerical count becomes larger in centimetres.
9. cm/s to m/s divides by one hundred
Centimetres per second become metres per second by dividing the distance numerator by one hundred while keeping the time denominator unchanged.
Worked example: 500 cm/s=5 m/s.
Checking question: The converted rate should be smaller numerically because metres are bigger units.
10. cm/s to km/h has two stages
First convert centimetres into metres, then metres per second into kilometres per hour. The combined multiplier for cm/s to km/h is 0.01×3.6=0.036.
Worked example: 500 cm/s=5 m/s=18 km/h.
Checking question: A one-step conversion can be checked by passing through m/s.
11. m/min to km/h combines minutes and kilometres
At a fixed rate of v metres per minute, sixty minutes gives 60v metres in one hour. Divide the distance by 1000 for kilometres, producing 0.06v km/h.
Worked example: 300 m/min=300×0.06=18 km/h.
Checking question: Alternatively divide by sixty to 5 m/s then multiply by 3.6.
12. km/h to m/min uses sixty minutes per hour
One kilometre is 1000 metres, and one hour is sixty minutes. Therefore v km/h becomes v×(1000/60) metres per minute.
Worked example: 18 km/h=18×1000/60=300 m/min.
Checking question: Reconvert 300 m/min by 0.06 to 18 km/h.
13. A speed comparison needs common units
Comparing 5 m/s and 20 km/h by their bare numerals is wrong. Convert one into the other’s unit first.
Worked example: 5 m/s=18 km/h, so 20 km/h is faster.
Checking question: State which unit was used for the final comparison.
14. Exact fractions are often preferable
The factor 3.6 is exact, but some other unit conversions yield repeating decimals. Keeping fractions or clearly rounded outputs reduces unnecessary error.
Worked example: 1 km/h=(5/18) m/s exactly. The decimal 0.2777… m/s is a recurring representation.
Checking question: Do not round a unit factor prematurely when a multi-step problem follows.
15. Distance equals speed multiplied by time
For constant speed, total distance is the rate multiplied by the matching duration. The units should cancel to leave a length.
Worked example: 12 m/s for twenty-five seconds covers 300 metres.
Checking question: Write (m/s)×s=m to verify the dimension.
16. Time equals distance divided by speed
When constant speed and distance are given, dividing the length by its rate returns a duration. The time unit follows the rate denominator.
Worked example: At 5 m/s, traversing 125 metres takes 25 seconds.
Checking question: Check by multiplying twenty-five seconds by five metres per second.
17. Speed equals distance divided by time
When distance and duration are stated, divide them in compatible units, then convert to whichever speed unit the question requests.
Worked example: A runner covers 180 metres in thirty seconds: 6 m/s or 21.6 km/h.
Checking question: Both results must describe the same run.
18. Minutes must become fractional hours in km/h calculations
A duration of thirty minutes is 0.5 hours, not 0.30 hours. A quarter hour is 0.25 and forty-five minutes is 0.75.
Worked example: At 72 km/h for fifteen minutes, distance=72×0.25=18 km.
Checking question: Convert minutes by dividing by sixty.
19. An hour-and-minute clock value is not a decimal duration
The notation 1 h 30 min represents 1.5 hours, while 1.30 hours as a decimal represents one hour and eighteen minutes. This distinction matters in travel calculations.
Worked example: At 60 km/h for 1 h 30 min, distance is ninety kilometres.
Checking question: Do not multiply 60 by 1.30 to represent the intended ninety minutes.
20. The conversion factor direction matters
Students sometimes use 3.6 correctly but in the wrong direction. Estimate how fast the motion sounds in each unit before calculating.
Worked example: 90 km/h=25 m/s, whereas 90 m/s=324 km/h. The same numeral represents very different rates.
Checking question: Label the starting and target units above the conversion arrow.
21. A speed can be less than one
A rate need not be an integer. A movement of 50 centimetres per second equals 0.5 m/s and 1.8 km/h.
Worked example: 50 cm/s ÷100=0.5 m/s.
Checking question: Fractional rates are valid even when a story uses whole object distances.
22. Two speed stages need separate distances
If different speeds apply during different durations, calculate each segment’s distance and add. One speed cannot be used for the entire trip without an appropriate average or interval.
Worked example: Travel 40 km/h for one hour then 60 km/h for half an hour: distance 40+30=70 km.
Checking question: Build a two-row rate–time–distance table.
23. A rest stop contributes elapsed time but no extra travel
A stationary break does not add distance. If the problem asks for whole-trip average speed, include the break in the denominator; if moving-only average, exclude it.
Worked example: Travel 60 km in 1.5 moving hours and rest 0.5 hours: full-trip average=60/2=30 km/h.
Checking question: State clearly which time interval the result uses.
24. Average speed is not generally the simple mean of rates
The correct average is total distance divided by total relevant time. A simple average of two speeds works for equal-duration stages, not necessarily equal-distance stages.
Worked example: Cover 60 km at 60 km/h then 60 km at 40 km/h: total 120 km over 2.5 h gives 48 km/h.
Checking question: The naive mean 50 km/h would not match the actual total time.
25. A distance–time slope expresses a rate
For a straight segment on a distance–time graph, the vertical increase in distance divided by the horizontal time interval is the segment’s speed. Read the axis units first.
Worked example: A graph rises 30 km over half an hour, giving 60 km/h.
Checking question: Do not mistake the final distance coordinate for the speed.
26. Changing units does not change the physical motion
The same movement can be described as 10 m/s, 36 km/h, 600 m/min or 1000 cm/s. Only the numerical unit convention changes.
Worked example: A ten-metre-per-second movement covers thirty-six kilometres in an hour.
Checking question: Convert two ways and check that the distance in a known interval stays the same.
27. A 3.6 conversion is a consequence, not a magic trick
Derive km/h ↔ m/s from 1000 m/km and 3600 s/hour before using 3.6 as a shortcut. Understanding its origin makes the direction easier to remember.
Worked example: 1 m/s×3600 seconds per hour=3600 metres per hour=3.6 km/h.
Checking question: Explain both distance and time conversions in words.
28. An inverse route is a powerful self-check
Converting from km/h to m/s and back should reproduce the original rate, subject only to final rounding. Large disagreement reveals an arithmetic or direction mistake.
Worked example: 72 km/h→20 m/s→72 km/h.
Checking question: Keep enough decimal precision to avoid round-trip drift.
29. The answer should use the unit requested
A calculation yielding 5 m/s is not in km/h until converted to 18 km/h. A correct underlying speed can still lose credit if the final unit does not match the task.
Worked example: A question asking for km/h needs 18 km/h, not merely five, when the intermediate rate is 5 m/s.
Checking question: Circle the desired unit in the problem’s last sentence.
30. Misplaced zeros often come from the distance numerator
One kilometre is 1000 metres, not one hundred. One metre is 100 centimetres, not one thousand. Speed conversion may involve both choices at once.
Worked example: 2 km=2000 m=200,000 cm.
Checking question: Write a unit ladder before calculating cm/s from km/h.
31. Use a dimensional estimate to catch large errors
Before calculator use, predict whether the rate should be plausible. At a few metres per second, the value in km/h is a few tens.
Worked example: 5 m/s is approximately 18 km/h, not 1800 km/h.
Checking question: Check whether every zero has a justified unit conversion.
32. Negative numerical rates need interpretation
A signed velocity may indicate direction in later physics, but basic Secondary 1 speed is nonnegative magnitude. A negative answer from subtracting clock times in the wrong order does not describe the intended travel speed.
Worked example: From 09:10 to 09:40 is thirty positive minutes, not a negative duration.
Checking question: Keep directional displacement separate from speed magnitude.
33. School questions use idealised constant rates
Actual traffic, cycling and walking speeds vary. A word problem stating constant speed asks students to apply that mathematical model, not to infer live travel times in Bukit Timah.
Worked example: A fictitious bicycle at 12 km/h for 30 minutes travels six kilometres in the exercise.
Checking question: Do not treat any stated speed as a current journey estimate.
34. One correct conversion can support several units
Start with 5 m/s. From there convert to m/min by multiplying sixty, to cm/s by multiplying one hundred and to km/h by multiplying 3.6.
Worked example: 5 m/s=300 m/min=500 cm/s=18 km/h.
Checking question: Show each conversion arrow and check one route in reverse.
35. A clear rate table can reveal the first mistake
When students confuse units, record original distance, original time, converted distance, converted time and final rate. The first inconsistent row identifies whether 1000, 60 or 3600 was mishandled.
Worked example: For 36 km/h, use 36,000 m in 3600 s to obtain 10 m/s.
Checking question: One precise correction is more useful than repeating all the speed formulas.
36. A unit rate is not an absolute distance
Speed of 20 m/s describes how much distance would be covered in one second at a constant rate, not how far a journey actually goes without a duration.
Worked example: 20 m/s for ten seconds covers 200 m; for twenty seconds covers 400 m.
Checking question: Ask for the missing time before reporting a trip length.
97 worked speed-unit and distance clinics
Cover each answer. These examples deliberately vary the direction of conversion and the type of unit, then add some constant-speed distance and time questions. Keep the original unit, destination unit and any rounding instruction visible throughout.
Speed clinic 1: Convert 9 km/h to m/s.
Answer: 2.5 m/s. Reason: Divide by 3.6: 9÷3.6=2.5. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 2.5 m/s by 3.6 to recover 9 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 2: Convert 18 km/h to m/s.
Answer: 5 m/s. Reason: Divide by 3.6: 18÷3.6=5. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 5 m/s by 3.6 to recover 18 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 3: Convert 27 km/h to m/s.
Answer: 7.5 m/s. Reason: Divide by 3.6: 27÷3.6=7.5. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 7.5 m/s by 3.6 to recover 27 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 4: Convert 36 km/h to m/s.
Answer: 10 m/s. Reason: Divide by 3.6: 36÷3.6=10. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 10 m/s by 3.6 to recover 36 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 5: Convert 45 km/h to m/s.
Answer: 12.5 m/s. Reason: Divide by 3.6: 45÷3.6=12.5. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 12.5 m/s by 3.6 to recover 45 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 6: Convert 54 km/h to m/s.
Answer: 15 m/s. Reason: Divide by 3.6: 54÷3.6=15. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 15 m/s by 3.6 to recover 54 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 7: Convert 63 km/h to m/s.
Answer: 17.5 m/s. Reason: Divide by 3.6: 63÷3.6=17.5. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 17.5 m/s by 3.6 to recover 63 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 8: Convert 72 km/h to m/s.
Answer: 20 m/s. Reason: Divide by 3.6: 72÷3.6=20. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 20 m/s by 3.6 to recover 72 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 9: Convert 81 km/h to m/s.
Answer: 22.5 m/s. Reason: Divide by 3.6: 81÷3.6=22.5. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 22.5 m/s by 3.6 to recover 81 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 10: Convert 90 km/h to m/s.
Answer: 25 m/s. Reason: Divide by 3.6: 90÷3.6=25. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 25 m/s by 3.6 to recover 90 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 11: Convert 108 km/h to m/s.
Answer: 30 m/s. Reason: Divide by 3.6: 108÷3.6=30. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 30 m/s by 3.6 to recover 108 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 12: Convert 126 km/h to m/s.
Answer: 35 m/s. Reason: Divide by 3.6: 126÷3.6=35. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 35 m/s by 3.6 to recover 126 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 13: Convert 144 km/h to m/s.
Answer: 40 m/s. Reason: Divide by 3.6: 144÷3.6=40. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 40 m/s by 3.6 to recover 144 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 14: Convert 180 km/h to m/s.
Answer: 50 m/s. Reason: Divide by 3.6: 180÷3.6=50. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 50 m/s by 3.6 to recover 180 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 15: Convert 216 km/h to m/s.
Answer: 60 m/s. Reason: Divide by 3.6: 216÷3.6=60. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 60 m/s by 3.6 to recover 216 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 16: Convert 252 km/h to m/s.
Answer: 70 m/s. Reason: Divide by 3.6: 252÷3.6=70. This equals converting kilometres to metres and hours to seconds.
Independent check: Multiply 70 m/s by 3.6 to recover 252 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 17: Convert 1 m/s into km/h.
Answer: 3.6 km/h. Reason: Multiply metres-per-second by 3.6: 1×3.6=3.6.
Independent check: Divide the answer by 3.6 to return to 1 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 18: Convert 2 m/s into km/h.
Answer: 7.2 km/h. Reason: Multiply metres-per-second by 3.6: 2×3.6=7.2.
Independent check: Divide the answer by 3.6 to return to 2 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 19: Convert 2.5 m/s into km/h.
Answer: 9 km/h. Reason: Multiply metres-per-second by 3.6: 2.5×3.6=9.
Independent check: Divide the answer by 3.6 to return to 2.5 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 20: Convert 3 m/s into km/h.
Answer: 10.8 km/h. Reason: Multiply metres-per-second by 3.6: 3×3.6=10.8.
Independent check: Divide the answer by 3.6 to return to 3 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 21: Convert 4 m/s into km/h.
Answer: 14.4 km/h. Reason: Multiply metres-per-second by 3.6: 4×3.6=14.4.
Independent check: Divide the answer by 3.6 to return to 4 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 22: Convert 5 m/s into km/h.
Answer: 18 km/h. Reason: Multiply metres-per-second by 3.6: 5×3.6=18.
Independent check: Divide the answer by 3.6 to return to 5 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 23: Convert 6 m/s into km/h.
Answer: 21.6 km/h. Reason: Multiply metres-per-second by 3.6: 6×3.6=21.6.
Independent check: Divide the answer by 3.6 to return to 6 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 24: Convert 8 m/s into km/h.
Answer: 28.8 km/h. Reason: Multiply metres-per-second by 3.6: 8×3.6=28.8.
Independent check: Divide the answer by 3.6 to return to 8 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 25: Convert 10 m/s into km/h.
Answer: 36 km/h. Reason: Multiply metres-per-second by 3.6: 10×3.6=36.
Independent check: Divide the answer by 3.6 to return to 10 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 26: Convert 12 m/s into km/h.
Answer: 43.2 km/h. Reason: Multiply metres-per-second by 3.6: 12×3.6=43.2.
Independent check: Divide the answer by 3.6 to return to 12 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 27: Convert 15 m/s into km/h.
Answer: 54 km/h. Reason: Multiply metres-per-second by 3.6: 15×3.6=54.
Independent check: Divide the answer by 3.6 to return to 15 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 28: Convert 18 m/s into km/h.
Answer: 64.8 km/h. Reason: Multiply metres-per-second by 3.6: 18×3.6=64.8.
Independent check: Divide the answer by 3.6 to return to 18 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 29: Convert 20 m/s into km/h.
Answer: 72 km/h. Reason: Multiply metres-per-second by 3.6: 20×3.6=72.
Independent check: Divide the answer by 3.6 to return to 20 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 30: Convert 25 m/s into km/h.
Answer: 90 km/h. Reason: Multiply metres-per-second by 3.6: 25×3.6=90.
Independent check: Divide the answer by 3.6 to return to 25 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 31: Convert 30 m/s into km/h.
Answer: 108 km/h. Reason: Multiply metres-per-second by 3.6: 30×3.6=108.
Independent check: Divide the answer by 3.6 to return to 30 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 32: Convert 40 m/s into km/h.
Answer: 144 km/h. Reason: Multiply metres-per-second by 3.6: 40×3.6=144.
Independent check: Divide the answer by 3.6 to return to 40 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 33: Convert 30 m/min to m/s and km/h.
Answer: 0.5 m/s; 1.8 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 0.5 m/s by factor 3.6 gives 1.8 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 34: Convert 60 m/min to m/s and km/h.
Answer: 1 m/s; 3.6 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 1 m/s by factor 3.6 gives 3.6 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 35: Convert 90 m/min to m/s and km/h.
Answer: 1.5 m/s; 5.4 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 1.5 m/s by factor 3.6 gives 5.4 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 36: Convert 120 m/min to m/s and km/h.
Answer: 2 m/s; 7.2 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 2 m/s by factor 3.6 gives 7.2 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 37: Convert 150 m/min to m/s and km/h.
Answer: 2.5 m/s; 9 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 2.5 m/s by factor 3.6 gives 9 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 38: Convert 180 m/min to m/s and km/h.
Answer: 3 m/s; 10.8 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 3 m/s by factor 3.6 gives 10.8 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 39: Convert 240 m/min to m/s and km/h.
Answer: 4 m/s; 14.4 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 4 m/s by factor 3.6 gives 14.4 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 40: Convert 300 m/min to m/s and km/h.
Answer: 5 m/s; 18 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 5 m/s by factor 3.6 gives 18 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 41: Convert 360 m/min to m/s and km/h.
Answer: 6 m/s; 21.6 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 6 m/s by factor 3.6 gives 21.6 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 42: Convert 480 m/min to m/s and km/h.
Answer: 8 m/s; 28.8 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 8 m/s by factor 3.6 gives 28.8 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 43: Convert 600 m/min to m/s and km/h.
Answer: 10 m/s; 36 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 10 m/s by factor 3.6 gives 36 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 44: Convert 750 m/min to m/s and km/h.
Answer: 12.5 m/s; 45 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 12.5 m/s by factor 3.6 gives 45 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 45: Convert 900 m/min to m/s and km/h.
Answer: 15 m/s; 54 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 15 m/s by factor 3.6 gives 54 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 46: Convert 1200 m/min to m/s and km/h.
Answer: 20 m/s; 72 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 20 m/s by factor 3.6 gives 72 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 47: Convert 1500 m/min to m/s and km/h.
Answer: 25 m/s; 90 km/h. Reason: Divide by 60 for m/s, or multiply by 0.06 for km/h.
Independent check: Converting 25 m/s by factor 3.6 gives 90 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 48: Convert 10 cm/s to m/s and km/h.
Answer: 0.1 m/s; 0.36 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 10×0.036=0.36. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 49: Convert 20 cm/s to m/s and km/h.
Answer: 0.2 m/s; 0.72 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 20×0.036=0.72. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 50: Convert 25 cm/s to m/s and km/h.
Answer: 0.25 m/s; 0.9 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 25×0.036=0.9. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 51: Convert 40 cm/s to m/s and km/h.
Answer: 0.4 m/s; 1.44 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 40×0.036=1.44. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 52: Convert 50 cm/s to m/s and km/h.
Answer: 0.5 m/s; 1.8 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 50×0.036=1.8. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 53: Convert 75 cm/s to m/s and km/h.
Answer: 0.75 m/s; 2.7 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 75×0.036=2.7. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 54: Convert 100 cm/s to m/s and km/h.
Answer: 1 m/s; 3.6 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 100×0.036=3.6. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 55: Convert 125 cm/s to m/s and km/h.
Answer: 1.25 m/s; 4.5 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 125×0.036=4.5. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 56: Convert 150 cm/s to m/s and km/h.
Answer: 1.5 m/s; 5.4 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 150×0.036=5.4. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 57: Convert 200 cm/s to m/s and km/h.
Answer: 2 m/s; 7.2 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 200×0.036=7.2. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 58: Convert 250 cm/s to m/s and km/h.
Answer: 2.5 m/s; 9 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 250×0.036=9. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 59: Convert 300 cm/s to m/s and km/h.
Answer: 3 m/s; 10.8 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 300×0.036=10.8. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 60: Convert 500 cm/s to m/s and km/h.
Answer: 5 m/s; 18 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 500×0.036=18. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 61: Convert 750 cm/s to m/s and km/h.
Answer: 7.5 m/s; 27 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 750×0.036=27. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 62: Convert 1000 cm/s to m/s and km/h.
Answer: 10 m/s; 36 km/h. Reason: Divide the centimetre rate by 100 to obtain m/s, then multiply by 3.6 for km/h.
Independent check: The combined cm/s→km/h factor is 0.036, so 1000×0.036=36. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 63: A hypothetical vehicle travels at 36 km/h for 15 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 9 km; speed 10 m/s. Reason: Convert 15 min to 15/60 h; distance=36×15/60=9 km. Separately divide speed 36 by 3.6.
Independent check: Recompute distance using 10 m/s over 900 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 64: A hypothetical vehicle travels at 54 km/h for 20 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 18 km; speed 15 m/s. Reason: Convert 20 min to 20/60 h; distance=54×20/60=18 km. Separately divide speed 54 by 3.6.
Independent check: Recompute distance using 15 m/s over 1200 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 65: A hypothetical vehicle travels at 72 km/h for 30 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 36 km; speed 20 m/s. Reason: Convert 30 min to 30/60 h; distance=72×30/60=36 km. Separately divide speed 72 by 3.6.
Independent check: Recompute distance using 20 m/s over 1800 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 66: A hypothetical vehicle travels at 90 km/h for 12 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 18 km; speed 25 m/s. Reason: Convert 12 min to 12/60 h; distance=90×12/60=18 km. Separately divide speed 90 by 3.6.
Independent check: Recompute distance using 25 m/s over 720 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 67: A hypothetical vehicle travels at 45 km/h for 40 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 30 km; speed 12.5 m/s. Reason: Convert 40 min to 40/60 h; distance=45×40/60=30 km. Separately divide speed 45 by 3.6.
Independent check: Recompute distance using 12.5 m/s over 2400 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 68: A hypothetical vehicle travels at 18 km/h for 50 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 15 km; speed 5 m/s. Reason: Convert 50 min to 50/60 h; distance=18×50/60=15 km. Separately divide speed 18 by 3.6.
Independent check: Recompute distance using 5 m/s over 3000 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 69: A hypothetical vehicle travels at 108 km/h for 10 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 18 km; speed 30 m/s. Reason: Convert 10 min to 10/60 h; distance=108×10/60=18 km. Separately divide speed 108 by 3.6.
Independent check: Recompute distance using 30 m/s over 600 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 70: A hypothetical vehicle travels at 60 km/h for 45 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 45 km; speed 16.66666667 m/s. Reason: Convert 45 min to 45/60 h; distance=60×45/60=45 km. Separately divide speed 60 by 3.6.
Independent check: Recompute distance using 16.66666667 m/s over 2700 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 71: A hypothetical vehicle travels at 24 km/h for 30 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 12 km; speed 6.66666667 m/s. Reason: Convert 30 min to 30/60 h; distance=24×30/60=12 km. Separately divide speed 24 by 3.6.
Independent check: Recompute distance using 6.66666667 m/s over 1800 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 72: A hypothetical vehicle travels at 80 km/h for 15 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 20 km; speed 22.22222222 m/s. Reason: Convert 15 min to 15/60 h; distance=80×15/60=20 km. Separately divide speed 80 by 3.6.
Independent check: Recompute distance using 22.22222222 m/s over 900 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 73: A hypothetical vehicle travels at 96 km/h for 25 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 40 km; speed 26.66666667 m/s. Reason: Convert 25 min to 25/60 h; distance=96×25/60=40 km. Separately divide speed 96 by 3.6.
Independent check: Recompute distance using 26.66666667 m/s over 1500 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 74: A hypothetical vehicle travels at 120 km/h for 20 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 40 km; speed 33.33333333 m/s. Reason: Convert 20 min to 20/60 h; distance=120×20/60=40 km. Separately divide speed 120 by 3.6.
Independent check: Recompute distance using 33.33333333 m/s over 1200 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 75: A hypothetical vehicle travels at 48 km/h for 75 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 60 km; speed 13.33333333 m/s. Reason: Convert 75 min to 75/60 h; distance=48×75/60=60 km. Separately divide speed 48 by 3.6.
Independent check: Recompute distance using 13.33333333 m/s over 4500 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 76: A hypothetical vehicle travels at 30 km/h for 60 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 30 km; speed 8.33333333 m/s. Reason: Convert 60 min to 60/60 h; distance=30×60/60=30 km. Separately divide speed 30 by 3.6.
Independent check: Recompute distance using 8.33333333 m/s over 3600 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 77: A hypothetical vehicle travels at 84 km/h for 35 minutes. Find distance in km and the same speed in m/s.
Answer: Distance 49 km; speed 23.33333333 m/s. Reason: Convert 35 min to 35/60 h; distance=84×35/60=49 km. Separately divide speed 84 by 3.6.
Independent check: Recompute distance using 23.33333333 m/s over 2100 seconds, then convert metres to kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 78: Which is faster, 5 m/s or 20 km/h?
Answer: 20 km/h. Reason: 5 m/s=18 km/h.
Independent check: Compare only after using a common unit. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 79: Which is faster, 6 m/s or 20 km/h?
Answer: 6 m/s. Reason: 6×3.6=21.6 km/h.
Independent check: 21.6 is greater than twenty. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 80: 36 km/h in m/min?
Answer: 600 m/min. Reason: 36,000 metres in sixty minutes.
Independent check: Also 10 m/s×60. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 81: 36 km/h in cm/s?
Answer: 1000 cm/s. Reason: 36 km/h=10 m/s=1000 cm/s.
Independent check: Check 1000 cm/s=10 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 82: 5 m/s in cm/s?
Answer: 500 cm/s. Reason: Multiply by 100.
Independent check: The time unit stays seconds. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 83: 5 m/s in m/min?
Answer: 300 m/min. Reason: Multiply by sixty.
Independent check: Five metres every second gives three hundred each minute. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 84: 10 cm/s in km/h?
Answer: 0.36 km/h. Reason: 10 cm/s=0.1 m/s; ×3.6=0.36.
Independent check: Keep zeros and decimal placement visible. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 85: 1 m/min in km/h?
Answer: 0.06 km/h. Reason: 60 metres in one hour =0.06 km.
Independent check: Do not treat metres as kilometres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 86: 12 m/s for 25 seconds: distance?
Answer: 300 m. Reason: 12×25.
Independent check: Units (m/s)×s become metres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 87: 125 m at 5 m/s: time?
Answer: 25 seconds. Reason: 125÷5.
Independent check: Check 5×25=125 metres. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 88: 180 m in thirty seconds: speed in m/s and km/h?
Answer: 6 m/s and 21.6 km/h. Reason: 180÷30=6; 6×3.6=21.6.
Independent check: Both rate descriptions represent the same run. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 89: 60 km at 60 km/h then 60 km at 40 km/h: moving average?
Answer: 48 km/h. Reason: Two stages take 1 and 1.5 hours; 120/2.5=48.
Independent check: Do not average 60 and 40 without time weighting. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 90: Vehicle travels 60 km in two hours and rests one hour: whole-trip average?
Answer: 20 km/h. Reason: Total 60 km over 3 hours.
Independent check: Moving average alone would be thirty. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 91: 72 km/h for one quarter hour: distance?
Answer: 18 km. Reason: One quarter hour is fifteen minutes.
Independent check: 72×0.25=18. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 92: A speed reads 2 m/s. Can you infer total distance without duration?
Answer: No. Reason: Different times produce different distances.
Independent check: Rate alone does not fix journey length. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 93: A 1 h 30 min journey at 60 km/h covers?
Answer: 90 km. Reason: 1 h 30 min =1.5 h.
Independent check: Do not treat as 1.30 decimal hours. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 94: 24 km/h to m/s to two decimal places?
Answer: 6.67 m/s. Reason: 24/3.6=6.666…
Independent check: Rounded report is approximate, not an exact equality. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 95: 15 m/s to km/h?
Answer: 54 km/h. Reason: 15×3.6=54.
Independent check: Return 54÷3.6=15. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 96: 300 m/min equals what in km/h?
Answer: 18 km/h. Reason: 300×60=18,000 m/hour=18 km/h.
Independent check: It equals 5 m/s. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Speed clinic 97: Convert 100 cm/s to km/h.
Answer: 3.6 km/h. Reason: 100 cm/s=1 m/s.
Independent check: One metre per second is 3.6 km/h. Change the rate or the duration and repeat the conversion with the reverse relationship, rather than copying a displayed calculator answer.
Four home investigations that show the rate units
Recreate the same speed in four units
Take 10 m/s. Convert to 600 m/min by multiplying sixty, to 1000 cm/s by multiplying one hundred and to 36 km/h by multiplying 3.6. Show that every statement describes the same physical distance per suitable time interval.
Try a changed rate once the model is removed. Ask the pupil to choose the conversion direction and explain the factor before calculating.
Compare two rates without guessing from numerals
Write 5 m/s and 20 km/h on two cards. Convert 5 m/s to 18 km/h before comparison. The 20 km/h value is faster even though its displayed numeral is larger under a different unit convention. Repeat with 6 m/s and 20 km/h.
Try a changed rate once the model is removed. Ask the pupil to choose the conversion direction and explain the factor before calculating.
Build the factor 3.6 from first principles
Write one kilometre equals 1000 metres and one hour equals 3600 seconds. Divide 3600 by 1000 for the m/s-to-km/h factor. Reverse that factor for km/h-to-m/s. Ask the student to explain why the same physical speed gets a larger numeral in km/h.
Try a changed rate once the model is removed. Ask the pupil to choose the conversion direction and explain the factor before calculating.
Find distance by two unit routes
Take 72 km/h for 15 minutes. First calculate 72×0.25=18 kilometres. Then convert speed to 20 m/s and duration to 900 seconds; distance is 18,000 metres, which equals eighteen kilometres. Agreement confirms both unit conversions.
Try a changed rate once the model is removed. Ask the pupil to choose the conversion direction and explain the factor before calculating.
A four-week plan for dependable rate conversions
Week 1: distance and time unit foundations
Revise 1000 metres per kilometre, 100 centimetres per metre, sixty seconds per minute and 3600 seconds per hour. Convert simple lengths and durations independently.
Use the student’s own school chapter sequence. A clear calculation with a reverse conversion and a labelled unit is more valuable than a long list of unreviewed keystrokes.
Week 2: km/h and m/s
Derive the factor 3.6, practise conversions in both directions and check every result by reversing it. Use friendly rates such as 18,36,54 and 72 km/h.
Use the student’s own school chapter sequence. A clear calculation with a reverse conversion and a labelled unit is more valuable than a long list of unreviewed keystrokes.
Week 3: m/min and cm/s
Introduce alternative numerator and denominator units. Compare speeds stated in different units only after making them compatible.
Use the student’s own school chapter sequence. A clear calculation with a reverse conversion and a labelled unit is more valuable than a long list of unreviewed keystrokes.
Week 4: full word problems and averages
Combine constant-rate distance calculations, mixed units, short journeys and rest intervals. Identify the requested rate and relevant time, then retest errors after several days.
Use the student’s own school chapter sequence. A clear calculation with a reverse conversion and a labelled unit is more valuable than a long list of unreviewed keystrokes.
How a small group can target a specific speed misconception
One student may use ×3.6 for km/h to m/s, another may convert one kilometre into only one hundred metres, and a third may treat 30 minutes as 0.30 hours. The incorrect results have different causes. A tutor can locate the first faulty conversion and repair it directly.
The eduKateSG Secondary 1 small-group tutorial reference describes weekly 90-minute learning for three students near Sixth Avenue MRT. An independent unseen conversion after feedback gives a clearer view of progress than copied calculations. Confirm current timetable and suitability directly.
Frequently asked questions
What is the exact conversion from km/h to m/s?
Multiply by 5/18, equivalently divide by 3.6.
How do I convert m/s to km/h?
Multiply by 3.6.
Why does 3.6 appear in speed conversion?
There are 1000 metres in a kilometre and 3600 seconds in an hour, giving factor 3600/1000.
How do I convert m/s to m/min?
Multiply by sixty, because a minute contains sixty seconds.
How do I convert m/min to m/s?
Divide by sixty.
How do I convert cm/s to m/s?
Divide by one hundred, since one metre contains one hundred centimetres.
How do I convert cm/s to km/h?
Divide by one hundred to get m/s, then multiply by 3.6. The combined factor is 0.036.
How do I convert km/h to m/min?
Multiply by 1000 metres per kilometre and divide by sixty minutes per hour.
Can I compare 5 m/s and 20 km/h directly?
No. Convert 5 m/s to 18 km/h, then 20 km/h is faster.
Is 1 hour 30 minutes equal to 1.30 hours?
No. It equals 1.5 hours; decimal 1.30 hours is one hour plus 0.30 hour, or eighteen minutes.
How do I calculate average speed across a rest stop?
Total distance divided by the complete elapsed time if the question asks for whole-trip average, including the stop.
What if my answer has recurring decimals?
Keep sufficient precision, then round to the requested number of decimal places and write an appropriate unit.
Is this part of Secondary 1 G2 Mathematics?
Yes. The MOE G2 syllabus explicitly includes speed in km/h, m/min, m/s and cm/s and conversion between units.
What is the most common speed-unit mistake?
Using the 3.6 factor in the wrong direction or confusing sixty minutes with one hundred minutes.
How can parents help check a conversion?
Ask the child to derive the relationship from metres per kilometre and seconds per hour, then reverse the final result.
What can small-group tuition diagnose?
Whether the wrong answer came from time conversion, distance conversion, rate direction, calculator precision or the choice of moving versus total time.
Official syllabus and connected G2 Mathematics articles
The MOE G2 Mathematics syllabus lists the Secondary 1 speed and rate-unit objectives. The unchanged eduKateSG small-group reference describes the teaching format. Further explanations include:
- Rate, speed, distance, time and units
- Journey timetables, rest stops and averages
- Unit prices, flow rates and work rates
- Arithmetic with signed numbers and brackets
- Reasonable answers and approximation errors
The best speed conversion is one the learner can explain using distance and time units. When the factor is understood, 3.6 stops being an arbitrary number and becomes an efficient, checkable shortcut.