Describing Motion Around Us
Position and displacement
Tell the distance something travels from how far it really moved.
Start with what you know. You are sitting in a train. Your friend sits opposite you. Is your friend moving? To you, no: your friend stays in the same seat. To a farmer standing in a field outside, yes: your friend is rushing past. Both are right. Whether something is moving depends on who is looking, and from where.
The reference point. So before we say anything about motion, we pick a fixed place to measure from. This is the reference point, also called the origin, written O. An object is moving if its position from O changes with time. It is at rest if its position from O stays the same.
Where is it? To say where something is, give two things:
- how far it is from O (in metres);
- which side of O it is.
On a straight line there are only two sides. We call one side + (usually to the right) and the other side – (to the left). Choose once, then keep the same choice for the whole problem.
Simple kinds of motion. Real motion is messy, so we study simple kinds first:
- linear: along a straight line, like a car on a straight road;
- circular: round a circle, like a merry-go-round;
- oscillatory: back and forth, like a swing.
Two time words. An instant is one reading of the clock: 'at 10 o'clock'. A time interval is the time between two readings: 'from 10 to 10:30'.
The most important pair in this chapter.
- Distance = how much you walked. Count every metre, whichever way you went.
- Displacement = where you ended up, compared with where you started, and in which direction.
Example: you walk to school, but first go to a friend's house and a shop on the way. Your distance is the whole wandering path. Your displacement is one straight arrow from home to school. Both are measured in metres.
Three walks, one picture. You walk 4 m, then 3 m more:
- straight on: you end up 4 + 3 = 7 m away;
- turning back: you end up 4 – 3 = 1 m away;
- turning at a right angle: you end up 5 m away (the long side of a right-angled triangle).
The distance is 7 m every time. Only the displacement changes. The picture tells you whether to add, subtract or use the triangle.
The athlete. She runs 100 m forward from O to A, then 60 m back to B.
- Distance = 100 + 60 = 160 m.
- Displacement = 40 m forward (+), because she ended 40 m from where she began.
Three rules to remember.
- Distance and displacement are equal only if you never turn back.
- If you turn back, the displacement is smaller than the distance. It is never bigger.
- If you come back to the start, the displacement is zero, however far you walked. A father who walks to the shop and back twice has walked a long way, but his displacement is zero.
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