Observe the linear and non-linear distance–time graphs of a rocket travelling at both constant and changing velocities. Calculate the average and instantaneous velocities of the rocket over different time intervals. Notice what happens to the average and instantaneous velocities as the time intervals become smaller. Work out the relationship between these velocities and the gradients of secants and tangents. This learning object is a combination of two objects in the same series.
Objective
Students interpret the gradient of a graph, and the gradient of the tangent to a curve, as being the rate of change of the function.
Students identify that a linear function produces a straight line graph.
Students identify that a non-linear function produces a curved graph.
Students predict that the average and instantaneous velocity of a linear function will always be the same at any given point on the graph.
Students apply the concept of a limit in the context of the rate of change of a function.
Students apply the first principles method to differentiate basic polynomial functions.
Curriculum Information
Education Type
K to 12
Grade Level
Grade 8, Grade 9, Grade 10
Learning Area
Mathematics
Content/Topic
Patterns and Algebra
Patterns and algebra
Intended Users
Learners, Students
Competencies
Copyright Information
Copyright
Yes
Copyright Owner
Education Sevices Australia
Conditions of Use
Use
Technical Information
File Size
0 bytes
File Type
application/x-rar
Software/Plug-in Requirements
Adobe Flash Player - http://get.adobe.com/flashplayer/
