To calculate instantaneous velocity, you need to find the derivative of the position function. For the given function F(T) = 5T^3 - 2T^2 - 48, the derivative is F'(T) = 15T^2 - 4T. To find the instantaneous velocity at T = 12 seconds, substitute 12 into the derivative, resulting in F'(12) = 15(12)^2 - 4(12). The derivative represents the slope of the tangent line, indicating the instantaneous rate of change at that specific point in time. Understanding this concept is crucial for applying instantaneous velocity in various contexts.