Suppose there is the following situation:
Blocks $A$ and $B$, with masses $m_A$ and $m_B$, are connected by a
light spring on a horizontal, frictionless table. When block $A$ has
acceleration $a_A$, then block $B$ has, by Newton’s second and third
laws, acceleration $-a_A\frac{m_A}{m_B}$.
What does it mean for block $B$ to have a negative acceleration? Since the blocks are connected by a spring, does not block $B$ move in the same direction as block $A$?
Best Answer
Acceleration is a vector, so $-a_A$ denotes an acceleration with the same magnitude as $a_A$, but in the opposite direction.
As for the second part, imagine that I place the two blocks down at rest, but far apart such that the spring is stretched beyond it's natural length. The spring will apply a force on each block towards the midpoint, causing them to move towards each other- opposite directions.