# Differential calculus: linear graphs

TLF ID L7819

Observe the linear distance–time graph of a rocket travelling at a constant velocity. Calculate the average and instantaneous velocity of the rocket over different time intervals. Notice how as each time interval becomes smaller the rocket's average velocity is equivalent to its instantaneous velocity. Work out how the gradient of the distance–time graph is related to the average and instantaneous velocities. This learning object is one in a series of ten objects. Some objects in the series are also packaged as combined learning objects.

#### Educational details

Key learning objectives
• Students interpret the gradient of a graph as being the rate of change of the function.
• Students identify that a linear function produces a straight line graph.
• Students determine that the average and instantaneous velocity of an object represented by a linear function will always be the same at any given point on the graph.
Educational value
• Demonstrates the connection between average and instantaneous velocity and the rate of change of a linear function.
• Provides opportunities for students to calculate the average and instantaneous velocity of a rocket between different time intervals.
• Features graphs for students to interpret visual representations of average and instantaneous velocities.
• Summarises key statements related to linear graphs and average and instantaneous velocities.
• Displays feedback for correct and incorrect answers.
Year level

11; 12

Learning area
• mathematics
Strand
• Mathematics/Algebra
Student activity
• Interactives;
• Experiment;
• Analysis;
• Modelling;
• Multiple choice questions

#### Other details

Contributors
• Script writer
• Educational validator
• Organisation: Professor Graham Jones
• Technical implementer
• Subject matter expert
• Organisation: Howard Reeves
• Address: Lindisfarne TAS 7015 Australia
• Educational validator
• Organisation: Doctor Paul White
• Address: Strathfield NSW 2135 Australia
• Publisher
• Date of contribution: 20 Sep 2013
• Organisation: Education Services Australia
• Address: Melbourne VIC 3000 Australia
• URL: http://www.esa.edu.au/
Access profile
• Colour independence
• Device independence
• Hearing independence
Learning resource type
• Interactive Resource
Browsers
• Microsoft Internet Explorer - minimum version: 8.0 (MS-Windows) - maximum version: 9.0 (MS-Windows)
• Firefox - minimum version: (MS-Windows)
• Safari - minimum version: 5.1 (MacOS)
Operating systems
• MacOS - minimum version: 10.6
• MS-Windows - minimum version: XP - maximum version: 7
Rights
• © Education Services Australia Ltd, 2013, except where indicated under Acknowledgements.

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