Four Questions That Sound Alike

You'll learnto tell a motion problem's four questions apart by the shape of their answers before any calculus happens, to keep the displacement separate from the position and the distance travelled separate from both, and to read a speed off a velocity vector rather than off an acceleration.

A motion problem asks four questions in almost the same words, and three of them are separated before any calculus happens, by the shape of the answer. Where is it and how far did it move are vectors. How far did it travel and how fast is it going are numbers. Half the lost marks in this topic are a pair offered where a single number was asked for, or a single number offered where a pair was, and those are wrong before their values are examined at all.

8 STEPS · 6 QUICK CHECKS · TWO OF THE FOUR ANSWERS ARE VECTORS · v1

travelled is the length of the path · moved is the length of the arrow

Before you start

What you're looking at

One plane, drawn at equal scale on both axes, so a length on screen is a length in the problem. A particle walks a curved path; a ring marks where it started and a filled dot is where it is now.

The question

Four things can be asked about this motion — where it is, how far it moved, how far it travelled, and how fast it is going. Which of them are vectors, and which are numbers?

Watch for

The arrow at the particle is its velocity, and the arrow's length is its speed. Watch that arrow vanish at the moment the path turns back on itself — and watch the straight arrow from the start get shorter while the path keeps getting longer.

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