Delta-v (physics)

In general physics, delta-''v'' is a change in velocity. 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 (Δv) or scalar (Δ''v''). In either case it is equal to the acceleration (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 (impulse), where: $\Delta \mathbf = m \Delta \mathbf$, where $\mathbf$ is momentum and m is mass.
Physical quantities

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