You already know unit rates and constant speed: 120 miles in 3 hours is 40 miles per hour. Physics uses the same idea, measured in SI units: distance in meters (m), time in seconds (s), so speed comes out in meters per second (m/s).
Key idea
Average speed is the total distance divided by the total time: $$s = \dfrac{d}{t}$$ Rearranged, $d = s\,t$ and $t = \dfrac{d}{s}$.
Why it works
Speed answers the question "how many meters each second?" If you run 100 m in 20 s at a steady pace, every second covers the same share: $100 \div 20 = 5$ meters each second. When the pace changes, the average speed is the steady speed that would cover the same distance in the same time.
Worked example: A sprint
In 2009 Usain Bolt ran 100 m in 9.58 s. What was his average speed?
- Use $s = \dfrac{d}{t}$ with $d = 100\,\mathrm{m}$ and $t = 9.58\,\mathrm{s}$.
- $s = \dfrac{100\,\mathrm{m}}{9.58\,\mathrm{s}} \approx 10.4\,\mathrm{m/s}$.
- He started from rest, so his top speed was higher than this average.
Answer: About $10.4\,\mathrm{m/s}$
Worked example: A trip in two parts
A bus drives 60 km at 60 km/h, then hits traffic and drives the next 60 km at 30 km/h. What is its average speed for the whole trip?
- Time for part 1: $t_1 = \dfrac{60\,\mathrm{km}}{60\,\mathrm{km/h}} = 1\,\mathrm{h}$.
- Time for part 2: $t_2 = \dfrac{60\,\mathrm{km}}{30\,\mathrm{km/h}} = 2\,\mathrm{h}$.
- Total distance $120\,\mathrm{km}$, total time $3\,\mathrm{h}$.
- $s = \dfrac{120\,\mathrm{km}}{3\,\mathrm{h}} = 40\,\mathrm{km/h}$.
Answer: $40\,\mathrm{km/h}$, not 45 km/h
Common mistake
Averaging the two speeds: $(60 + 30) \div 2 = 45$ km/h. That would only work if the bus spent equal times at each speed. Here it spent twice as long crawling at 30 km/h, so the average leans toward 30. Check: always divide the total distance by the total time.
Light is the fastest thing there is: about 300,000 km every second. Even so, sunlight takes about 8 minutes and 20 seconds to cover the 150 million km to Earth, so you see the Sun as it was a few minutes ago.