Final answer:
The missing variable in the equation 'v_f² = v_i² + 2a * Δ * x' is the initial position (x_o), which should be part of the displacement term in the standard kinematic equation 'v_f² = v_i² + 2a(x - x_o)'.
Step-by-step explanation:
The equation given is v_f² = v_i² + 2a * Δ * x, which is based on one of the kinematic equations that describe motion. To find out which variable is missing, we need to analyze the provided equation and compare it to the standard form of the kinematic equation, which is v_f² = v_i² + 2a(x - x_o). In the equation provided, we have variables representing the final velocity (v_f), the initial velocity (v_i), and the acceleration (a). The variable representing the displacement, which should be x, seems to be partially represented by Δ * x. However, in the standard form, the displacement is represented as (x - x_o), where x_o is the initial position and x is the final position. Thus, the missing variable is the initial position (x_o). This formula is essential as it allows us to calculate the final velocity from the initial velocity, acceleration, and displacement without involving time.