Read this section to learn how to apply the Chain Rule. Work through practice problems 1-8.
If we know the position of an object at every time, then we can determine its speed. The formula for
speed comes from the distance formula and looks a lot like it, but with derivatives.
Proof: The speed of an object is the limit, as , of . (Fig. 6 )
Exercise 10: Find the speed of the object whose location at time is when and .
Practice 7: Show that an object whose location at time is has a constant speed. (This object is moving on a circular path).
Practice 8: Is the object whose location at time is travelling faster at the top of the ellipse ( at ) or at the right edge of the ellipse (at )?