Rest, motion and the reference point

Is the person next to you moving?

You sit in a moving bus. The person next to you sits too. Are they moving?

Compared to the road, yes: they move along with the bus. Compared to you, no: they stay right next to you. Both answers are right. We must always say what we compare with. That thing is called the reference point.

Rest and motion

An object is at rest if its position does not change with time, compared to the reference point. It is in motion if its position does change.

Think of a passenger in a moving train.

• Compared to the seat, the passenger is at rest.
• Compared to the trees outside, the passenger is moving.

The passenger did not change. Only the reference point changed.

Walking in a train

Now the passenger gets up and walks towards the front. Compared to the train, they move only as fast as they walk. Compared to the ground, the train carries them too, so the two speeds add.

You should find that the ground line is always steeper than the train line when the passenger walks forward. With the walking speed equal to minus the train's speed, the passenger stands still compared to the ground.

Watch out. 'At rest' almost always means 'at rest compared to the ground'. Even a house moves with the turning Earth.

A worked example

A train runs at $15\ \text{m/s}$. A passenger walks towards the front at $1.5\ \text{m/s}$ for $20\ \text{s}$. How far does the passenger move compared to the train, and compared to the ground?

1. Compared to the train. Only the walking counts: $1.5\ \text{m/s} \times 20\ \text{s} = 30\ \text{m}$.
2. Compared to the ground. The speeds add: $(15\ \text{m/s} + 1.5\ \text{m/s}) \times 20\ \text{s} = 330\ \text{m}$.
3. So one walk gives two answers, one for each reference point.

Practise with new numbers

Try it in Python

The program works out the example.

Remember these

• Rest and motion are always compared with a reference point.
• The same object can be at rest compared to one thing and moving compared to another.
• Walking forward in a train, your speed over the ground is the train's speed plus your walking speed.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. You sit in a moving car. Name one thing you are at rest compared to, and one thing you are moving compared to.

2. Two trains run side by side at the same speed. How does a passenger in one see the other train?

3. A boy walks towards the front of a bus at $1\ \text{m/s}$. The bus moves at $12\ \text{m/s}$. How fast does he move compared to the road?

4. Is a tree at rest? Explain.