Assumptions & Limitations
One of the most important assumption made in this assignment is, I assumed that the swimmer kept on swimming and swimming in the same time period and completes the same distance. This is a crucial element which helped me form the graph and the equation, without this assumption, the sinusoidal function would not be the most appropriate function. With the assumption i made above, a sinusoidal function is the best and most appropriate function for this case.
There are certain limitations which have helped to make the graph and the function reasonable. The limitations are:
There are certain limitations which have helped to make the graph and the function reasonable. The limitations are:
- There cannot be negative values in time and distance. Which limits the graph to go beyond the first quadrant.
- This is a reasonable limitation in real life situation. There is no way that the swimmer can swim a negative distance, or spend negative time periods.
- Another limitation i have made in the equation of the derivative of distance (velocity over time) is that the time cannot be negative. There is velocity values, however there is no negative time value!
PREDICTION
The graphs of distance and velocity are two reasonable sinusoidal graphs. However, if there is no assumptions, the graph will look a lot more different.
If the swimmer stops at 100 meters but he still spend the same period of time to swim 50 meters. Then the graph will be a piece wise sinusoidal function!
If the swimmer kept on swimming, but the time period changes, the graph will not be a sinusoidal function.
If the swimmer stops at 100 meters but he still spend the same period of time to swim 50 meters. Then the graph will be a piece wise sinusoidal function!
If the swimmer kept on swimming, but the time period changes, the graph will not be a sinusoidal function.