Learning objects Differential calculus: non-linear graphs

TLF ID L7820

Observe the non-linear distance–time graph of a rocket travelling at a changing 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 approaches its instantaneous velocity. Use the slider to change the points where the secant intersects the curve and observe the gradient calculator. Work out the relationship between average and instantaneous velocities and the gradients of secants and tangents. 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 identify that a non-linear function produces a curved graph.
  • Students apply the concept of a limit in the context of the rate of change of a non-linear function.
  • Students interpret the gradient of the tangent to a curve as being the rate of change of the function.
  • Students apply the first principles method to differentiate basic polynomial functions.
Educational value
  • 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 non-linear graphs and average and instantaneous velocities.
  • Allows students to manipulate where the secant intersects the curve in order to establish relationships between secant and gradient tangents 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;
  • Data manipulation and interpretation

Other details

Contributors
  • Script writer
  • Educational validator
  • Name: Professor Graham Jones
  • Address: Broadbeach QLD 4218 Australia
  • Technical implementer
  • Subject matter expert
  • Name: Howard Reeves
  • Address: Lindisfarne TAS 7015 Australia
  • Educational validator
  • Name: 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
  • 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.