Final answer:
The condition ∆v = 0 indicates constant or unchanged velocity, which occurs when no net force is acting on an object, in compliance with Newton's first law. The equation ∆KE + ∆PE = 0 upholds the conservation of energy, showing constant mechanical energy in the presence of conservative forces. These principles are foundational to understanding motion and energy in physics.
Step-by-step explanation:
When we say ∆v = 0, we are stating that there is no change in velocity, which implies that the velocity is constant. This can be due to the fact that when no net force acts on an object (signifying ∆ = 0 or zero net force), the object will maintain its state of motion according to Newton's first law of motion. This also means that if an object is at rest (zero velocity), it will stay at rest, and if it's moving at a constant velocity, it will continue moving at that velocity unless acted upon by a force.
Considering the other equation ∆KE + ∆PE = 0, this represents the principle of conservation of energy for conservative forces. It implies that the total mechanical energy (sum of kinetic and potential energy) of a system is constant if only conservative forces are doing work. In a case where there is no change in kinetic or potential energy, it implies no work is being done on the system, which correlates with the condition of constant velocity when no net force is present.
An object undergoing a round trip will have zero net displacement, but its speed during the trip is not zero. This scenario further emphasizes that a constant or zero velocity can occur under various circumstances.