Consider the free fall of a particle at position with height . Given that and the time for the particle to travel from to is .
- What is the time traveled from to , in seconds?
- What is the height , in meters?
First, we draw a graph of the particle
We knew that . So, the area of and must be the same, hence the equation
The time traveled from to is .
is the area of the graph
In my opinion, it would be more complicated if we used elementary formula to solve this problem. Worse, they are easier to make mistakes and harder to look for errors. If one can use the graph wisely, we can optimize the problem and tackle it effectively.