Problem : Find the position function for an elephant on a tightrope if the elephant's path goes as follows: (1) the elephant begins 5 ft to the right of the origin (center of the tight rope), (2) the elephant moves left at a steady pace for 3 minutes and ends up 2 ft left of the origin, (3) the elephant stays still at that spot for 1 minute, and (4) the elephant moves right at a steady pace for another 2 minutes and ends up 1 foot to the right of the origin.

Our first task in tackling this problem is to write down everything we already know about the position function x(t). From (1) we know that x(0) = 5. (2) tells us that x(3) = - 2, and (3) indicates that x(t) = - 2 for all t between 3 and 4. Finally, from (4) we know that x(6) = 1. Because the elephant always moves "at a steady pace," we can plot these known points on the graph of the position function and fill in the rest by drawing straight lines between them. The final position function, defined for t valued between 0 and 6, looks like: Unlike other position functions we've discussed thus far, this one cannot be written as a single equation--algebraically it must be defined in pieces. For this reason it's a little easier to represent the solution graphically.

Problem : Plot the position function given by x(t) = - gt2 + h for g = 9.8 and h = 40.