The first line is a convenient way to tie the program to the parameter s values. At left some are drawn. It appears that the longest velocity vector the fastest part of the ride occurs in the middle of each section. The same idea may be used to see the acceleration vectors. Then enter and run this program which works the same as the last program.
Lower graph is the speed vs. time.
The exploration above shows a method for visualizing the velocity and acceleration vectors of a vector equation. The general procedure is to use the LINE operation of a graphing calculator to draw the velocity or acceleration vectors at various points of the curve. The graphs may be produced with a simple program on any graphing calculator with a LINE operation. Then run the same program. Teaching Suggestion Usually watching the graph being drawn is more helpful than seeing the final graph.