## Speed, distance, time

This topic covers interpreting distance-time graphs; drawing distance-time graphs from given data; and defining speed as the distance covered in a certain time.

The resources in BT STEM Crew can be used either in sequence or flexibly as an introduction to a topic, or for a quick activity.

Introduce the topic of speed, distance and time with a short starter film, discussing how boat speed depends on the wind speed, and on the direction of the wind compared to the direction the boat needs to go to the next marker. Test students' knowledge with an engaging interactive. Our differentiated worksheets reinforce learning objectives for this topic.

## Film

## Interactive quiz

The Land Rover BAR team analyse data to help them increase performance. Challenge your students on speed, distance and time to see if they can help to improve the boat's performance when racing.

## Worksheets

Test students' learning with these differentiated worksheets.

### Worksheet 1

11-14 lower

### Worksheet 2

11-14 higher

### Worksheet 3

14-16

## Teacher's notes

### Starter

Write the following on the board: walking, running, cycling, champion sprinter, champion cyclist, cargo ship, racing yacht.

Challenge students to suggest typical speeds for these things. If they suggest speeds in mph, write these values up but also convert to metres per second (1 mph = 0.45 m/s). Students note their suggestions and keep them for the plenary.

### Suggested activity

Put D-T graph on the board and challenge students to 'walk it' by adjusting their speed (only a qualitative match is expected). Or use a motion sensor and data logger to detect their speed and build up a D-T graph on-screen as they move.

### Plenary

Following use of worksheets, students should have a better idea of the typical speeds – they update their lists, and are challenged to draw a line for each speed on a D-T graph.

### Further ideas/ STEM Club ideas

Build model boats (simple ones will do) and use a fan to race them along a trough of water. Measure distances and times and draw D-T graphs for the different boats.

## Curriculum links

### England

**KS3 NC Science**

Physics, describing motion:

- Speed and the quantitative relationship between average speed, distance and time (speed = distance ÷ time)
- The representation of a journey on a distance-time graph

**GCSE Science**

Edexcel

- 2.6 Recall and use these equations (average) speed = distance ÷ time, distance travelled = average speed x time
- 2.7 Analyse distance/time graphs including determination of speed from the gradient
- Recall some typical speeds encountered in everyday experience for wind and sound, and for walking, running, cycling and other transportation systems

AQA

- The speed of a moving object is rarely constant. When people walk, run or travel in a car their speed is constantly changing.
- Typical values may be taken as: walking ̴ 1.5 m/s running ̴ 3 m/s cycling ̴ 6 m/s. Students should be able to recall typical values of speed for a person walking, running and cycling as well as the typical values of speed for different types of transportation systems.
- For an object moving at constant speed the distance travelled in a specific time can be calculated using the equation: distance travelled = speed × time s = v t
- If an object moves along a straight line, how far it is from a certain point can be represented by a distance–time graph.
- The speed of an object can be calculated from the gradient of its distance–time graph.

OCR Gateway Combined

- P2.1b describe how to measure distance and time and use these to calculate speed
- P2.1e relate changes and differences in motion to appropriate distance-time, and velocity-time graphs; interpret lines and slopes
- P2.1g calculate average speed for non-uniform motion

**KS3 NC Maths**

Ratio, proportion and rates of change; algebra:

- Use compound units such as speed to solve problems
- Model situations or procedures using graphs
- Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

**KS4 NC Maths**

Algebra; ratio, proportion and rates of change:

- Plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
- Use compound units such as speed
- Change freely between related standard units (e.g. time, length) and compound units (e.g. speed) in numerical and algebraic contexts

**GCSE Mathematics**

AQA

- G3.7 Understand and use compound measures.
- N6.12 Discuss, plot and interpret For example distance–time graphs (which may be graphs. non-linear) modelling real situations.

Edexcel

- A14 plot and interpret and graphs of non-standard functions in real contexts to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
- A15 calculate or estimate gradients of graphs and areas under graphs and interpret results in cases such as distance-time graphs, velocity-time graphs
- R1 Change freely between related standard units (e.g. time, length) and compound units (e.g. speed) in numerical and algebraic contexts
- R11 use compound units such as speed

OCR

- A4.3 Interpret information presented in a range of linear and non-linear graphs, including travel (distance/time) graphs. NB speed calculations will not be required
- S7.8 Understand and use rates and compound measures, for example speed.

### Wales

**KS3 Science**

- Understand the forces in devices and their relationship to work done and power

**GCSE Physics**

WJEC

- Learners should be able to demonstrate and apply their knowledge and understanding of motion using speed, velocity and acceleration

### Scotland

**Fourth level Science**

- Use appropriate methods to measure, calculate and display graphically the speed of an object, and show how these methods can be used in a selected application
- Relate the motion of an object to the forces acting on it by making accurate measurements of speed and acceleration

**National 4 Physics**

- Use of an appropriate relationship to solve problems involving speed, distance, and time.
- Determination of average and instantaneous speed. Interpretation of speed-time graphs to describe motion including calculation of distance

### Northern Ireland

**KS3 Science & Technology**

- Make connections between two sets of data or events and describe the relationship between them in own words, for example, speed and braking distances, etc; how would the relationship be affected if something changed

**GCSE Physics**

- 1.1.1 investigate experimentally the quantitative relationships between average speed, distance and time
- 1.1.3 calculate rate of change of speed (acceleration) as change of speed divided by time taken