Describing motion · Quantitative
Speed
A fly crosses your view in half a second. A plane takes a full minute to cross the same patch of sky. Which one is actually faster — and what would you have to know to say?
Start here
The slow-looking one covers 250 metres every second.
The fly is 30 cm from your eye and takes half a second to cross your view. The plane is 10 km up and takes a minute to cross the same patch of sky. One of them would cross a football pitch in less than half a second, and it is not the fly.
So what would you have to know to say which is faster?
How fast something looks depends on how far away it is. Speed does not. It is one number built from two measurements — how far, and how long — and until you have both you have nothing to compare.
A sprinter covers 100 m in 12 s. A marathon runner covers 42 000 m in 7200 s. The sprinter travels far less ground and is far faster. Distance alone settles nothing and time alone settles nothing; the two have to be put together.
The light gates · the timer gives you a time, nothing else
You own both measurements.
The trolley rolls off the ramp and breaks two beams. The clock starts at the first gate and stops at the second. You choose how far apart the gates are.
Commit first. You raise the ramp so the trolley rolls faster. What does the gate timer read?
Gate separation
Gate timer
Speed
not measured — you work it out
| Run | Ramp | Distance | Time |
|---|
Three runs, three different times, and the same distance every time. That scatter is why one reading is never enough — and the mean of the three times is what you divide into.
You changed the setup between runs, so these times are not repeats of one measurement, and the mean of them is not a time for anything. Set the gates and the ramp once, then take three runs.
Key fact
A speed is two measurements made into one number: distance ÷ time. On its own, neither measurement can tell you which is faster.
Writing it down · the shape of this relationship
Speed = distance ÷ time
m with s gives m/s
km with h gives km/h
and the two cannot be mixed
The triangle
Cover the one you want
Distance is on its own at the top, with the other two side by side underneath. Cover it and you are left with s × t — multiply.
Speed sits underneath, with distance above it. Cover it and you are left with d over t — divide.
Time sits underneath, with distance above it. Cover it and you are left with d over s — divide.
Two things side by side means multiply. One thing over another means divide.
Five lines, every time · CFIFA
A trolley crosses gates 1.20 m apart in 0.84 s.
Step 0 of 5
Convert
1.20 m stays 1.20 m · 0.84 s stays 0.84 s
The gap is already in metres and the time is already in seconds, so there is nothing to convert.
Formula
s = d ÷ t
Cover s on the triangle: d sits over t, so you divide.
Insert
s = 1.20 m ÷ 0.84 s
Distance on top, because distance is on top of the triangle.
Fine-tune
1.20 ÷ 0.84 = 1.4285…
Metres divided by seconds leaves metres per second.
Answer
s = 1.43 m/s
Two decimal places, and the unit.
Five lines, every time · CFIFA
A car covers 1.8 km of motorway in 90 s.
Step 0 of 5
Convert
1.8 km × 1000 = 1800 m
The formula wants metres, and a kilometre is a thousand of them, so multiply by 1000.
Formula
s = d ÷ t
Cover s on the triangle: d sits over t, so you divide.
Insert
s = 1800 m ÷ 90 s
The converted distance goes in. The kilometre reading never does.
Fine-tune
1800 ÷ 90 = 20
Metres divided by seconds leaves metres per second.
Answer
s = 20 m/s
Insert 1.8 instead of 1800 and the answer comes out a thousand times too small.
Three words you have just used
Say what each one means out loud. Then turn the card and check yourself.
Three pairs · one of them is a dead heat
Work each one out before you choose.
Two things, both plausible, where the eye gives the wrong answer. Do the division first.
Pair 1
Pair 2 · the one from the top of the page
Pair 3 · different units
One of the three was a dead heat and the eye could not have told you which.
Think again
“I walked 100 m at 1 m/s, then ran 100 m at 5 m/s. So my average speed was 3 m/s.”
Halfway between 1 and 5 is 3, and the two distances are equal, so it looks safe. It is not. Walking 100 m at 1 m/s takes 100 s; running 100 m at 5 m/s takes 20 s. The whole journey is 200 m in 120 s, which is 1.67 m/s.
You spent five times as long walking as running, so the walk counts five times as much. That is why the answer sits close to walking pace and nowhere near 3 m/s. Average speed is always the total distance divided by the total time — never the average of the speeds.
“A speed camera tells you how fast you were going on the journey.”
It tells you how fast you were going over a few metres of it. That is an instantaneous speed — measured over a stretch so short that the speed has no time to change — and it can be far above or far below the average for the trip. Average-speed checks on motorways exist because the two numbers are different: they time you between two gantries and work out distance ÷ time, which no single camera can do.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
A trolley crosses two light gates 1.5 m apart in 0.60 s. What is its speed?
Rung 2 · The one that catches people
A runner covers the first 200 m in 40 s, then the next 200 m in 60 s. What is their average speed for the whole 400 m?
Rung 3 · Explain
A student times a trolley over the same 1.20 m three times and gets 0.81 s, 0.84 s and 0.90 s. Say what they should do with the three numbers before working out a speed, and why one run on its own is not good enough.
Rung 4 · Take it somewhere new
You have a tape measure and a phone stopwatch, and you want the speed of someone walking down a corridor. Describe how you would measure it, and say what the biggest source of error is and how you would cut it down.
Key note
Speed = distance ÷ time, in metres per second. It turns two measurements into one number, so any two journeys can be compared. Finishing first is not the same as travelling fastest, and average speed is total distance ÷ total time.
Going further
A roadside speed camera measures you over about half a metre of road. An average-speed camera measures you over two kilometres. Both are doing distance ÷ time, and they can disagree completely: you can pass every camera at exactly the limit and still have averaged more than the limit in between, or crawl through a jam and pass one camera far too fast. Neither reading is a lie. A speed is only ever the speed over the stretch you divided by, and how long that stretch is changes the answer.
Before this lesson
- Nothing — this is where the unit starts.
At GCSE this becomes
- Acceleration, motion graphs that carry direction as well as size, and the equations of motion — all built on distance ÷ time.
Where to next
- Next: Distance–time graphs
- Previous: Fuels and energy resources
Energy at home
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