Original post by NonIndigenousI assume you know how to integrate. When you integrate, you end up with a "+C" constant. Then you substitute the upper and lower bound values (7 and 2) for "t", and subtract them from one other. That also means you subtract "C" from itself... effectively cancelling it out.
The displacement at "t=2" being "0" is relative. It depends where you draw the 'baseline', or in other words, where the graph crosses the y-axis. If the graph above instead crossed the y-axis where currently "t=2", the displacement at that point would technically be "0". I probably didn't explain that well earlier, since I've also not worked with things like this for a while now. If that were the case (instead of what it is in the question), the equation they provide would also be different. But it isn't. That might sound confusing, so think of it more simply:
- Just integrate the equation and substitute the upper and lower bounds into the equation. When you subtract the substituted equation of "2" from "7", you effectively obtain the displacement as if it where measured from "2", or in other words, as if "2" were the baseline.