Final answer:
Adding more force to a cart causes an increase in speed by directly affecting the acceleration, as depicted by pattern a) Speed increased as force was added. A free-body diagram can be used to illustrate the various forces at play, and other dynamic graphs like velocity-time can depict the relationship between force, acceleration, and speed.
Step-by-step explanation:
In accordance with Newton's second law of motion, the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. Thus, when more force is added to one side of the cart, the speed increases, given that acceleration has taken place and the object continues to move in the direction of the force applied. This is observed as pattern a) Speed increased as force was added.
To explain the effects with a free-body diagram, we can illustrate the forces acting on the object, such as gravity, normal force, applied force, and friction. The free-body diagram helps us to understand the net force acting on the object. From the free-body diagram, we can then derive the other graphs: position, velocity, and acceleration graphs, which all relate to one another. For example, a uniform acceleration results in a straight line in a velocity versus time graph, showcasing a constant increase in speed.
When you engage the simulation mentioned, you will notice that as you increase the applied force, the velocity-time graph shows a steeper slope, which corresponds to an increase in acceleration and therefore an increase in speed if mass remains constant.