Final answer:
The graph depicting the relationship between temperature and kinetic energy in a substance's phase would show a direct proportionality, with temperature increasing linearly with kinetic energy. Both total kinetic energy and total momentum would remain constant over time if no external forces influence the system.
Step-by-step explanation:
The graph that shows the relationship between temperature and kinetic energy in a single phase of matter would be a straight line, indicating that there is a direct proportionality between the two variables. This is because when the temperature of a substance increases, the average kinetic energy of its molecules also increases. This relationship can be understood when considering that temperature is a measure of the average kinetic energy per molecule in a system. Therefore, if all other factors remain constant, the increase in temperature will result in increased kinetic energy of the molecules.
Similarly, a graph plotting the total kinetic energy of a collection of particles against time, assuming no energy is lost or gained from outside the system, would show a constant value over time. This is based on the principle of conservation of energy, which states that in an isolated system, the total energy remains constant. The total momentum of a system is also conserved, meaning that if no external forces act upon the system, the total momentum graph against time will also be a constant line.