Answer
Graph (2) and graph (3) correspond to a physically impossible situation.
Work Step by Step
The slope of the position versus time graph is the velocity.
We know that the velocity of the center of mass does not change during a collision.
Therefore, on each graph, the line that starts at the origin and continues in a straight line after the collision corresponds to the center of mass.
In graph 2, the slope of the line for the center of mass is greater than both the slopes of the line segments corresponding to the two bodies. This means that the velocity of the center of mass is greater than the velocities of both bodies in the system.
In graph 3, the slope of the line for the center of mass is greater than both the slopes of the line segments corresponding to the two bodies. This means that the velocity of the center of mass is greater than the velocities of both bodies in the system.
However, this situation is physically impossible since the velocity of the center of mass can not be greater than both velocities of the two bodies in the system.
