Two particles $A, B$ are travelling along parallel straight paths. At some point, the velocity of $A$ exceeds that of $B$. Does this necessarily mean that the acceleration of $A$ is greater than the acceleration of $B$?
If you look at the $v - t$ graph of the two particles, the lines would intersect. Probably, starting off, the velocity of $B$ would be greater, but since the slope of the velocity of $A$ would be greater it would intersect with the graph of $B$ and exceed it. I couldn't think of any other situation. So, my conclusion was that the acceleration has to be greater. But my textbook says otherwise. How come?
EDIT: This is question 13 from chapter 2 in Resnick halliday physics.
To clarify: the problem does NOT assume that initally A's velocity was lower than B's. (See comments)