Parametric Curves, Part 12 (distance traveled and speed functions)

Distance traveled and speed functions for straight-line motion. For an arbitrary function h(t) that we assume is increasing in value from 0 to 1 over the (time) interval [0,1], find the distance traveled function dist(t) and the speed function speed(t). Make use of Manipulate, Graphics, and Line in Mathematica to make a growing triangle and use the Pythagorean theorem at an arbitrary value of t to do find dist(t) for this example of straight-line motion. Intuitive introduction to the derivative operator that, in this physical example, gives the function speed(t).