Vinitial

Vinitial is a term used in physics and engineering to denote the initial velocity of an object at the start of a time interval or process. The subscript i indicates initial, distinguishing it from later velocities such as Vfinal. In Cartesian coordinates, Vinitial can be represented as a vector (Vx0, Vy0, Vz0) or, in simple cases, as a magnitude V0.

In classical mechanics, the initial velocity serves as a starting condition for motion. If acceleration a is constant, the velocity at time t is v(t) = Vinitial + a t, and the position is x(t) = x0 + Vinitial t + 0.5 a t^2. The initial velocity thus influences the subsequent trajectory, along with forces and boundary conditions.

In orbital mechanics and spaceflight, Vinitial describes the spacecraft’s velocity at the moment a maneuver begins. The required change in velocity, or delta-v, depends on Vinitial; after a burn, Vfinal = Vinitial + Δv. In simulations and trajectory planning, Vinitial is an input parameter that sets the starting conditions for numerical integrations and optimization.

Notation varies by field, with alternatives such as v0 or v_i used in some texts. The exact interpretation of Vinitial can differ, so it is important to consult the specific model or context. Overall, Vinitial is a foundational parameter in describing motion from a known starting state. See also initial velocity, delta-v, vis-viva equation, and Newtonian mechanics.