Final answer:
The 'a' in F = ma, representing acceleration, is the variable indicating 'a rate of change of a rate of change of position'. Acceleration is the second derivative of position, and in Newton's second law, relates force to mass and the rate of change of velocity.
Step-by-step explanation:
The part of the equation F = ma that represents "a rate of change of a rate of change of position" is the acceleration (a). Acceleration itself is defined as the rate at which velocity changes with time, and velocity is the rate at which position changes with time. Hence, acceleration is the second derivative of position with respect to time, making it a rate of change of a rate of change. Within the context of Newton's second law, acceleration is directly proportional to the net force applied (F) and inversely proportional to the mass (m) of the object.
Newton's second law of motion in terms of momentum can be expressed as Fnet = Δ(mv) / Δt, where the change in momentum (Δ(mv)) over time (Δt) shows how force affects the motion of an object. When mass is constant, the change in momentum is essentially the mass times the change in velocity, which is the definition of acceleration, bringing us back to the formula Fnet = ma.
The significance of Newton's second law is that it quantifies the effect of forces on the motion of objects, providing a cornerstone for classical mechanics.