Final answer:
A graph of total momentum vs. time would be a horizontal line when the velocity is constant, reflecting constant momentum. When forces are applied, the slope would change indicating a change in momentum. The total kinetic energy graph remains constant if velocity is constant but will change as the square of velocity if velocity changes.
Step-by-step explanation:
To understand how the graphs of total momentum vs. time and total kinetic energy vs. time would look like, first, it's important to note that the change in momentum of an object is proportional to the force applied and the duration of its application. A constant velocity indicates that the momentum does not change over time, making the momentum vs. time graph a horizontal line since the momentum remains constant.
If we consider a system where the force is exerted over a span of time, resulting in a change in momentum, the graph would slope upwards or downwards depending on the direction of the force. In the cases where two objects interact through collision or gravity, the momentum is conserved, and the graph would reflect the appropriate conservation law. The total kinetic energy is directly proportional to the velocity squared, so if velocity is constant, the kinetic energy would also be depicted as a constant line on a graph vs. time. However, if velocity changes due to forces, the kinetic energy graph could potentially change with the square of the velocity.