I'm trying to understand a sample problem from a current (published 2011) high school physics textbook, but I really think the question is flawed. The task is to convert an acceleration-time graph (AT-graph) into a velocity-time graph (VT-graph). The AC-graph is given as:
Then the book gives the following instructions for finding velocities from accelerations:
Here's my first problem. Where did they get the formula $v=(\Delta a)(\Delta t)$? Isn't $\Delta a$ a more advanced concept called "jerk"? (a concept that this textbook never introduces, by the way). Shouldn't it be $\Delta v = a\Delta t$? And if so, we're not finding $v$ (which, correct me if I'm wrong, is impossible from the data given), but merely $\Delta v$.
Then they show the following calculations:
This chart is confusing to me. Is the time column an instant of time or a time interval? (I think it's a time interval). It seems to me that they're calculating $\Delta v$, not $v$, in which case it's impossible to draw a VT graph. But that's what they do next anyway:
Any feedback is appreciated.