Final answer:
Graphs for gravitational potential energy and kinetic energy of a ball thrown upwards would show a converse relationship, while the total energy remains constant, representing conservation of mechanical energy.
Step-by-step explanation:
To graphically represent the gravitational potential energy, kinetic energy, and total energy of a ball thrown straight up and caught as it comes down, we need to consider the height of the ball over time. Initially, when the ball is thrown, the kinetic energy is at its maximum while the gravitational potential energy is at a minimum. As the ball rises, its velocity decreases, so the kinetic energy decreases while the gravitational potential energy increases. Upon reaching the highest point, the ball's kinetic energy is zero and its potential energy is at maximum. The kinetic energy then increases again as the ball falls, trading potential energy for kinetic energy until it is caught, at which point the kinetic energy returns to zero.
During this whole process, in absence of air resistance, the total energy of the ball remains constant. This is because the sum of kinetic energy and potential energy remains the same at all points during the ball's flight, which is a representation of the conservation of mechanical energy.
The graph of total momentum versus time would be a flat line since momentum is conserved and there are no external forces (ignoring air resistance). A graph of total kinetic energy versus time would look like a parabola that peaks at the beginning and as the ball is caught.