Lesson 13: Introduction to Speed
BasicSpeed = distance ÷ time. For example, 60 km in 2 hours, speed = 60 ÷ 2 = 30 km/h. Learn speed formula and unit conversion.
- Speed = distance ÷ time
- Distance = speed × time
- Time = distance ÷ speed
文體小知識：速率的意義、公式、單位
§Text Passage
1Speed: how far something travels per unit time. For example, 30 km per hour, speed is 30 km/h. Faster speed means further in the same time.
2Speed formula: speed = distance ÷ time. v = d ÷ t. Distance in km or m, time in h or s, speed unit is km/h or m/s.
3Common speeds: walking ~4-5 km/h, cycling ~15 km/h, car ~50-80 km/h, high-speed rail ~200 km/h, airplane ~900 km/h.
1Summary 重點摘要
Speed = distance ÷ time. For example, 60 km in 2 hours, speed = 60 ÷ 2 = 30 km/h. Learn speed formula and unit conversion.
2Vocabulary cards Vocabulary
How fast
How far
How long
Kilometres per hour
Metres per second
Average speed over whole journey
Math rule
Measurement unit
3Step by step Steps
- Block 1: Speed FormulaThe speed formula is v = d ÷ t, distance divided by time. Example: a 100-metre race finished in 20 seconds gives speed = 100 ÷ 20 = 5 m/s, meaning 5 metres every second on average. Speed tells how far something travels in one unit of time; common units are m/s and km/h.
- Block 2: Known Speed and TimeWith speed and time known, find distance using d = v × t. Example: a car travelling at 60 km/h for 3 hours covers 60 × 3 = 180 km. You can picture 60 km/h as 60 kilometres each hour, so 3 hours means three lots of 60 kilometres, which is 180 kilometres.
- Block 3: Known Speed and DistanceWith speed and distance known, find time using t = d ÷ v. Example: two towns 120 km apart, driven at 40 km/h, take 120 ÷ 40 = 3 hours. Picture moving 40 kilometres each hour; it takes 3 hours to finish 120 kilometres, so the answer makes sense.
- Block 4: Unit ConversionSpeed units convert like this: 1 km/h = 1000 m ÷ 3600 s = 518 m/s. So km/h to m/s multiplies by 518, and m/s to km/h multiplies by 185. Example: 36 km/h = 36 × 518 = 10 m/s. To remember which fraction, check whether the answer should get bigger or smaller.
- Block 5: Average SpeedIf the pace changes during a journey, average speed = total distance ÷ total time; never just add the two speeds and halve. Example: 30 km/h for the first half and 60 km/h for the second half does not average to 45 km/h, because the two parts take different times and the slow part lasts longer.
- Block 6: Common ExampleExample: a car covers 100 km in 2 hours, so speed = 100 ÷ 2 = 50 km/h. If it keeps this speed for 5 hours, the distance = 50 × 5 = 250 km. Such questions chain the three quantities: find the speed first, then use it for the new distance, so practise all three forms of the formula.
4Diagrams Diagrams
5Worked example Example
Example: A car travels 180 km in 3 hours. What is its speed?
- Step 1: write the formula, speed = distance ÷ time, the basic relation in speed problems.
- Step 2: substitute the numbers, speed = 180 ÷ 3, with distance 180 km and time 3 hours.
- Step 3: work out 180 ÷ 3 = 60 to get the value of the speed.
- Step 4: attach the unit: km divided by hours gives km/h, so the speed is 60 km/h.
- Step 5: check — travelling 3 hours at 60 km/h covers 60 × 3 = 180 km, matching the question, so the answer is correct.
- Answer: Answer: the car's speed is 60 km/h, which means 60 kilometres every hour. In speed problems substitute into the formula, always write the unit km/h, and finish by multiplying speed by time to confirm the distance before the answer is complete.
6Common mistakes Mistakes
7Quick check Quick check
Q180 km in 2 hours. Speed?
Q2Speed 50 km/h, 4 hours. Distance?
Q3Distance 150 km, speed 50 km/h. Time?
Q436 km/h = ? m/s
Q5Speed formula?
8Recap Recap
- Speed = distance ÷ time
- Distance = speed × time
- Time = distance ÷ speed
- km/h to m/s: × 518
- Average speed = total distance ÷ total time