Lesson: Applications of Derivatives on Rectilinear Motion Mathematics • Third Year of Secondary School

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In this lesson, we will learn how to apply derivatives to problems of motion in a straight line.

Students will be able to

find the absolute extrema (maximum and minimum values) for displacement and velocity,
find the intervals over which a body has positive or negative velocity (increasing or decreasing displacement),
find the intervals over which a body has positive or negative acceleration (increasing or decreasing velocity),
find the instantaneous value(s) of displacement, velocity, or acceleration for a given value of one of the other quantities (displacement, velocity, or acceleration),
find the acceleration when velocity is given as a function of position (using the chain rule),
find the average speed over an interval when given displacement (specifically instances where the particle changes direction within the given time interval).