Speed (intro)

1Summary 重點摘要

Speed = distance ÷ time.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: What speed meansSpeed tells how far you travel in one unit of time: going 30 km in one hour gives a speed of 30 km/h, read as thirty kilometres per hour. Why invent such a quantity? Because neither distance nor time alone can compare journeys: if A covers 100 km in 2 hours and B covers 90 km in 1.5 hours, dividing each distance by its time gives 50 km/h and 60 km/h, and only then do we know B is faster. Speed links distance and time, so different journeys can be compared fairly. A common mistake is to think that the longer the distance, the greater the speed; comparing speeds requires looking at distance and time together and converting to kilometres per hour first.
2. Step 2: The formulaSpeed = distance ÷ time. For 100 km travelled in 2 hours, compute 100 ÷ 2. Why division? Because speed asks 'how far per hour', and sharing the whole distance equally among the hours is exactly the idea of equal sharing. The three quantities in the formula are linked: knowing any two gives the third. This lesson practises finding the speed; later come distance = speed × time and time = distance ÷ speed. For example, 240 km in 4 hours gives speed = 240 ÷ 4 = 60 km/h. A common mistake is to remember the formula backwards, dividing time by distance to get something like 4 ÷ 240; the reading 'kilometres per hour' — kilometres first, hours last — maps exactly onto distance divided by time.
3. Step 3: Substitute and computeWhen solving, first pick out the distance and the time from the question, write the expression, and only then calculate: 100 km in 2 hours gives speed = 100 ÷ 2 = 50, so the speed is 50 km/h. Why write the expression first? Because matching the distance with the time correctly prevents mixing up figures, especially when a question gives two journeys at once. The arithmetic itself is easy; the skill is picking out the right data — is the distance in kilometres or metres, is the time in hours or minutes — before substituting. For example, 3000 m in 6 minutes gives speed = 3000 ÷ 6 = 500 m/min. A common mistake is to cross-substitute the data of two vehicles, or to omit the unit; build the three-step habit: formula first, numbers next, unit last.
4. Step 4: Attach unitsThe unit follows from the units of distance and time: kilometres divided by hours is written km/h; metres divided by seconds is m/s; metres divided by minutes is m/min. Why do units matter as much as numbers? Because the same 50 means very different speeds: 50 km/h and 50 m/s differ by dozens of times, and an answer without a unit is incomplete and impossible to compare. km/h reads kilometres per hour and m/s reads metres per second, and both forms should be read and written fluently. For example, a treadmill showing 3 m/s runs at 3 metres every second, which is 180 metres a minute. A common mistake is to divide kilometres by minutes yet write km/h; the unit must match the units actually used, and km/h requires the time converted to hours first.
5. Step 5: Compare speedsComparisons need the same unit: car A at 60 km/h against car B at 50 km/h — in one hour A covers 60 km and B only 50, so A is faster. Why does a larger speed mean faster? Because speed means exactly the distance covered per unit of time; the more ground per hour, the faster. If the units differ, convert to one unit before comparing: 10 m/s as km/h is 10 metres each second, that is 10 × 3600 = 36000 metres per hour, which is 36 km/h. A common mistake is to compare bare numbers without looking at units, assuming 50 must beat 10, so 50 km/h surely beats 10 m/s; in fact 10 m/s = 36 km/h, which is indeed slower than 50 km/h, but only the conversion earns the right to that conclusion.
6. Step 6: Reverse checkAfter finding the speed, check backwards with distance = speed × time: at 50 km/h for 2 hours you cover 50 × 2 = 100 km, exactly the distance in the question, so the calculation stands. Why does reversing work? Because division and multiplication are inverse operations: the forward step divides distance by time, and the backward step multiplies speed by time, so the two confirm each other. For example, 3000 m in 6 minutes gives 500 m/min, and working back, 500 × 6 = 3000 m matches the question, making the answer trustworthy. One reverse pass firms up the formula and steadies the answer — a habit worth keeping in tests. A common mistake is to copy a number wrongly during the check, say writing 500 for 50; copy the original figures from the question and verify them one by one instead of rewriting from memory.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Speed = distance ÷ time
• Match the units: km/h, m/s
• A bigger speed number is faster
• Check: speed × time = distance
• Half an hour is 0.5 hours — convert before substituting