Saturday, 24 August 2013

If the velocity of particle $A$ exceeds that of $B$, is the acceleration of $A$ greater than $B$?

If the velocity of particle $A$ exceeds that of $B$, is the acceleration
of $A$ greater than $B$?

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?

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