# Relative Motion

In this worksheet, students will learn about relative motion and how trains and cars appear to be moving as they pass one another.

Key stage:  KS 3

Curriculum topic:   Physics: Motion and Forces

Curriculum subtopic:   Describing Motion

Difficulty level:

### QUESTION 1 of 10

Relative motion is all about motion in relation to a frame of reference. A frame of reference is the motion of an observer of the motion of an object. For example, you may be sitting by your window observing a taxi driving past your house. From your perspective, you are at rest and the taxi is moving. However, a passenger on the taxi would see you as moving.

An observer at a train station would see a fast train that does not stop at that station move past them at a speed of 250 mph. If the observer can see inside the train, a cup of coffee on a train table would be seen as moving at the same speed as the train. A passenger on the train, though, would perceive the same cup of coffee being at rest on the table.

If an observer can see a child throwing a ball to a friend in a moving train in the same direction as the speed of the train, it would seem that the ball is moving faster than the train, as the final speed of the ball would be the sum of the speed of the train and the speed that the child threw the ball at.

Let's make this clearer. Look at the diagram of a train floor and a ball. The speed of the ball with respect to the train is 5 m/s. The speed of the train with respect to the ground is 10 m/s, so if someone outside the train is watching the ball moving, they will see it moving at 15 m/s, which is the sum of the speed of the train and the speed of the ball (with respect to the train).

If the child throws the ball in the opposite direction, the observer would see the ball slowing down and maybe even move to the opposite direction, depending on the speed of the train and the speed the ball was thrown at. This is because speed is not only a number, but a vector, called velocity. A vector is represented by an arrow, the length of which indicates the size of the speed (e.g. 20 km/s), whereas the direction the arrow points towards indicates the direction of movement.

We will now explore relative motion further through the questions that follow.

What is relative motion?

Relative motion is any type of movement.

Relative motion is motion of an object by its own accord.

Relative motion is motion in relation to a frame of reference.

What is relative motion in relation to a frame of reference?

Motion of an object/person in relation to an observer.

Motion of a tennis ball in a tennis court.

Real time motion of an object.

Imagine you are sitting on the beach and a ship is speeding in the sea. You can see the ship and the captain. How does the captain appear to be moving in relation to an observer on the ship?

The captain appears to be moving at the same speed as the ship.

The captain appears to be at rest.

The captain appears to be moving at half the ship's speed.

Imagine you are sitting on the beach and a ship is speeding in the sea. You can see the ship and the captain. How does the captain appear to be moving in relation to you?

The captain appears to be moving at the same speed as the ship.

The captain appears to be at rest.

The captain appears to be moving at half the ship's speed.

What is velocity?

speed with direction

an arrow pointing left

a number

The diagram shows a train carriage moving to the right with a speed of 6 m/s. The person inside the carriage, at the back of the track, is moving to the right at a speed of 1 m/s.

You are an observer at rest by the side of the track the carriage is moving on.  What is the overall speed of the person on the track as it appears to you?

1 m/s

6 m/s

7 m/s

The diagram shows a train carriage moving to the right with a speed of 4 m/s. The person inside the carriage, at the back of the track, is moving to the left at a speed of 1 m/s.

You are an observer at rest by the side of the track the carriage is moving on.  What is the overall speed of the person on the track as it appears to you?

1 m/s

3 m/s

4 m/s

A cyclist is moving to the left at a speed of 15 m/s. The wind blows against the cyclist's movement at a speed of 5 m/s.

What will be the overall speed of the cyclist as it appears to an observer watching the cyclist from their house?

3 m/s

10 m/s

20 m/s

A child on a sleigh that is travelling at 1 m/s to the right throws a ball with a speed of 1.5 m/s at another child at rest in front of the sleigh.

What speed does the ball travel at?

1 m/s towards the child at rest

1.5 m/s towards the child at rest

2.5 m/s towards the child at rest

A child on a sleigh travelling at 1 m/s to the right throws a ball in the opposite direction (left) with a speed of 1.5 m/s.

What speed does the ball travel at?

0.5 m/s away from the child on the sleigh

1.5 m/s away from the child on the sleigh

• Question 1

What is relative motion?

Relative motion is motion in relation to a frame of reference.
EDDIE SAYS
Relative motion is motion in relation to a frame of reference.
• Question 2

What is relative motion in relation to a frame of reference?

Motion of an object/person in relation to an observer.
EDDIE SAYS
Relative motion is the motion of an object/person in relation to an observer.
• Question 3

Imagine you are sitting on the beach and a ship is speeding in the sea. You can see the ship and the captain. How does the captain appear to be moving in relation to an observer on the ship?

The captain appears to be at rest.
EDDIE SAYS
To an observer on the ship, the captain appears to be at rest.
• Question 4

Imagine you are sitting on the beach and a ship is speeding in the sea. You can see the ship and the captain. How does the captain appear to be moving in relation to you?

The captain appears to be moving at the same speed as the ship.
EDDIE SAYS
To you, the captain appears to be moving at the same speed as the ship.
• Question 5

What is velocity?

speed with direction
EDDIE SAYS
Velocity is a vector that shows speed as a number with the direction of motion.
• Question 6

The diagram shows a train carriage moving to the right with a speed of 6 m/s. The person inside the carriage, at the back of the track, is moving to the right at a speed of 1 m/s.

You are an observer at rest by the side of the track the carriage is moving on.  What is the overall speed of the person on the track as it appears to you?

7 m/s
EDDIE SAYS
To you, the person seems to be moving at the total speed of 6 + 1 = 7 m/s to the right.
• Question 7

The diagram shows a train carriage moving to the right with a speed of 4 m/s. The person inside the carriage, at the back of the track, is moving to the left at a speed of 1 m/s.

You are an observer at rest by the side of the track the carriage is moving on.  What is the overall speed of the person on the track as it appears to you?

3 m/s
EDDIE SAYS
To you, the person seems to be moving at the total speed of 4 – 1 = 3 m/s to the right.
• Question 8

A cyclist is moving to the left at a speed of 15 m/s. The wind blows against the cyclist's movement at a speed of 5 m/s.

What will be the overall speed of the cyclist as it appears to an observer watching the cyclist from their house?

10 m/s
EDDIE SAYS
The cyclist's velocity will be 10 m/s to the left.
• Question 9

A child on a sleigh that is travelling at 1 m/s to the right throws a ball with a speed of 1.5 m/s at another child at rest in front of the sleigh.

What speed does the ball travel at?

2.5 m/s towards the child at rest
EDDIE SAYS
The ball travels at 1 + 1.5 = 2.5 m/s towards the child at rest.
• Question 10

A child on a sleigh travelling at 1 m/s to the right throws a ball in the opposite direction (left) with a speed of 1.5 m/s.

What speed does the ball travel at?

0.5 m/s away from the child on the sleigh
EDDIE SAYS
The ball travels at 1 – 1.5 = -0.5 m/s, which means the snowball travels at 0.5 m/s away from the child on the sleigh.
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