1. The velocity problem.

If a ball is thrown up in the air with a velocity of 40 ft/sec, its height in feet after seconds is given by . Let us express this by defining a Maple command which expresses as a function of .

> s:=t->-16*t^2+40*t;

To find the average velocity for the time period beginning at sec, and lasting for 0.5 sec, we enter the following command.

> (s(2+.5)-s(2))/.5;

Submission:

Calculate the average velocity for the time period beginning at and lasting for

(b) 0.05 sec

Use these values to guess the instantaneous velocity at sec. Will the average velocity ever actually equal the instantaneous velocity? Precisely explain the relationship between average velocity and instantaneous velocity.

Submission Worksheet:

2. Velocity as the slope of a tangent line.

This is a continuation of the previous activity. At sec, the position is given by , so you can find an equation of the line passing through the point (2,16), with slope equal to the instantaneous velocity. (Recall that the equation of a line with slope through the point ( ) is given by .)

Plot this line and the graph of on the same plot. Indicate units on the horizontal and vertical axes (look up labels in help.)  What are the units of the slope of the line you plotted? What is the relationship between the line you plotted and the graph of the position function?

Submission worksheet: