Describing motion · Model
Relative motion
Your train is doing 100 km/h. A second train pulls alongside, also doing 100 km/h, and through the window it hangs there motionless. How fast is it going?
Start here
For a few seconds, the other train is parked.
Your train is doing 100 km/h. A second train pulls alongside, also doing 100 km/h. Through the window it hangs there, motionless, close enough to read a book over someone's shoulder. Then it edges ahead and slides away.
Commit. How fast is that train going?
Both of the first two answers are right, and neither is complete. 100 km/h measured from the platform. 0 km/h measured from your seat. The question was missing the only words that would let it have one answer: relative to what? Every speed in the last two lessons was secretly measured against the ground, and nobody said so because nobody needed to.
Every speed in the last two lessons was secretly measured against the ground — the corridor, the runway, the road. Nobody said so, because nobody needed to. As soon as the thing you measure from is itself moving, you do.
Same road, same two cars, three different answers
Change who is watching.
Nothing about the cars changes when you switch viewpoint, but the numbers do. What changes is which reading is the one you are sitting in — and that reading is always zero.
Commit first. Two cars both travel at 25 m/s in the same direction, side by side. What is the speed of one measured by the driver of the other?
A from the roadside
B from the roadside
B from car A
A from car B
The road from the roadside
One of the five readings is always zero — whatever you are sitting in, measured from where you are sitting. Nothing about either car changed to make it so.
Key fact
Every speed is measured relative to something. Say what it is, or the number does not mean anything.
Four passes · decide the direction first
How fast does one pass the other? Same way, subtract. Opposite ways, add.
Decide whether the two are going the same way or opposite ways before you touch the numbers.
Pass 1
Two trains both travel at 30 m/s in the same direction on parallel tracks, side by side. How fast does one pass the other?
Pass 2
The same two trains, still 30 m/s each, now travelling towards each other. How fast does one pass the other?
Pass 3
A car at 25 m/s overtakes a lorry doing 20 m/s. How fast does the car pass the lorry?
Pass 4
You walk at 1.5 m/s towards the front of a train that is doing 30 m/s. How fast are you moving relative to the ground?
Four passes, and not one of them was a multiplication. Relative speed is a sum or a difference — which is why this lesson has no formula triangle.
Think again
“The other train was doing 100 km/h and mine was doing 100 km/h the other way, so it went past me at 100 km/h.”
In one hour your train covers 100 km one way and the other covers 100 km the other way, so the gap between them closes by 200 km. From your seat, that train is doing 200 km/h.
You have felt the difference. A train overtaking yours on the next line takes ten seconds to slide past because the two speeds nearly cancel. A train coming the other way is a bang and a blur, and it is gone — same trains, same speeds, and 200 km/h between them instead of 5.
“Sitting still in a train seat, you are not moving.”
Relative to the seat, correct. Relative to the platform you are doing 100 km/h, relative to the Sun the whole train is doing about 30 km every second, and none of those answers is more true than the others. The question is only complete once a frame of reference is named — which is why every speed in physics quietly carries the words “relative to the ground” unless it says otherwise.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
A cyclist rides at 6 m/s. A bus going the same way overtakes at 14 m/s. What is the bus's speed relative to the cyclist?
Rung 2 · The one that catches people
A passenger sits still in her seat on a train travelling at 30 m/s. Which statement is true?
Rung 3 · Explain
Two trains passing in opposite directions are gone in a second, but a train overtaking yours on the next track seems to take forever. Explain both, using relative speed and numbers of your own choosing.
Rung 4 · Take it somewhere new
A plane flies at 250 m/s relative to the air. It flies 900 km east with a 50 m/s wind behind it, then straight back west against the same wind. Work out its speed relative to the ground on each leg, and explain why the round trip takes longer than it would with no wind at all.
Key note
Every speed is relative to something, and for ordinary questions that something is the ground. To find how fast one object passes another: same way, subtract; opposite ways, add. Changing who measures changes the number, never the object.
Going further
Sitting still, you are travelling about 30 km every second around the Sun, and you cannot feel any of it. That is not a trick of the senses: no experiment done inside a smoothly moving room can tell you how fast the room is going, or whether it is moving at all. Physicists spent two hundred years hunting for the one truly stationary thing to measure everything else against. There isn't one.
Before this lesson
Connects to
At GCSE this becomes
- Vectors and combining motions that carry direction, and — much later — the reason light refuses to play by these rules.
Where to next
Ask Mr Badmus AI
Not sure when to add and when to subtract?
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