Graphing swimming is a lot more complicated than it might seem. The only graph that is somewhat simple is if the swimmer swims at a constant pace throughout the whole time/race. This graph would be a straight line angling at about 45 degrees; or a sawtooth wave. The faster the swimmer, the more compressed horizontally the sawtooth wave becomes. The slower the swimmer, the more horizontally elongated the sawtooth wave becomes. By increasing the distance (50 meter pool), it would take longer to reach the peak of the graph. For this reason the graph would be vertically stretched if the distance was increased.
To make the graph look like a triangle you would have to go a constant pace back and forth. To make the triangle look like a sawtooth wave, you would have to go a constant pace to the other side of the pool. It is impossible to make it look like a square because no human could ever achieve a graph like that. To make it look like a sine curve you would have to increase and decrease your speed at certain intervals of your swim.
In regards to the two swimmers question, the swimmer swimming the long length of the pool will get to the other side twice as fast compared to the swimmer swimming the short distance. The amount of intersections in the graph is one. By the time the slow swimmer gets across the 25m, the fast swimmer will have gone to the other
wall and back. This is the intersection point. The paths of the two swimmers with intersect every time the slow swimmer gets to the other wall.
