Delta-v (physics)
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In general physics, delta-''v'' is a change in
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
. The Greek uppercase letter Δ (delta) is the standard mathematical symbol to represent change in some quantity. Depending on the situation, delta-''v'' can be either a
spatial vector In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors ac ...
(Δv) or
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...
(Δ''v''). In either case it is equal to the
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
(vector or scalar) integrated over time: *Vector version: \Delta \mathbf = \mathbf_1 - \mathbf_0 = \int^_ \mathbf \, dt *Scalar version: \Delta v = _1 - _0 = \int^_ a \, dt If acceleration is constant, the change in velocity can thus be expressed as: \Delta \mathbf = \mathbf_1 - \mathbf_0 = \mathbf \times \Delta t = \mathbf \times (t_1-t_0) where: *v0 or ''v''0 is initial velocity (at time ''t''0), *v1 or ''v''1 is subsequent velocity (at time ''t''1). Change in velocity is useful in many cases, such as determining the change in
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
(
impulse Impulse or Impulsive may refer to: Science * Impulse (physics), in mechanics, the change of momentum of an object; the integral of a force with respect to time * Impulse noise (disambiguation) * Specific impulse, the change in momentum per uni ...
), where: \Delta \mathbf = m \Delta \mathbf, where \mathbf is momentum and m is mass. Physical quantities {{physics-stub