initialvelocity

Initial velocity is the velocity of an object at the beginning of a specified time interval or process. It is a vector, characterized by both speed and direction, and is commonly denoted by u or v0. In kinematics it provides the initial conditions for motion; the velocity at time t is v = u + a t, where a is acceleration, and the position evolves as s = s0 + u t + 1/2 a t^2.

For projectile motion neglecting air resistance, the initial velocity components are u_x = v0 cos theta and u_y = v0 sin theta; the subsequent path depends on gravity g with vertical velocity v_y = u_y - g t. The range and time of flight are functions of v0 and theta.

In orbital mechanics, initial velocity at a point defines the orbit around a primary body; different initial velocities yield different orbital shapes, such as circular or elliptical trajectories. The concept is also central in experiments and simulations, where initial velocity sets the starting state from which motion is integrated.

Units are meters per second (m/s). Initial velocity is distinct from initial speed only in that it is directional; speed is its magnitude. In measurements, initial velocity can be determined from velocity-time data or derived from position-time data, and it may vary if acceleration is present.