Figure 9-34 shows four graphs of position versus time for two bodies and their center of mass. The two bodies form a closed, isolated system and undergo a completely inelastic, one-dimensional collision on an x-axis. In graph 1, are (a) the two bodies and (b) the center of mass moving in the positive or negative direction of the x-axis? (c) Which of the graphs correspond to a physically impossible situation? Explain.

Four graphs of position versus time for two bodies and their center of mass.

From the slopes of the lines in graph 1, we can conclude the direction of motion of the 2 bodies and their center of mass. From the characteristics of the center ofmass and the nature of the graph, we can find the graph which corresponds to a physically impossible situation.

From graph 1, we can infer that the slopes of the lines are positive.

Therefore, two bodies are moving in the positive direction of the x-axis.

From graph 1, we can infer that the slopes of the lines are positive.

Therefore, the center of mass of the bodies is moving in the positive direction of the x-axis.

For an isolated system, the center of mass of the given straight linegraph is betweenx and t. The center of the mass line should lie between the lines for two masses.

Therefore graph 2 and 3 corresponds to a physically impossible situation.