Delta-v (physics)

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For the special astrodynamical meaning see Delta-v.

In general physics, delta-v is simply the change in velocity. The Greek letter delta is a standard mathematical symbol to represent change (and can be thought of as a fulcrum with a beginning and ending state).

Depending on the situation, delta-v can be referred to as a spatial vector ( $\Delta \mathbf{v}\,$ ) or scalar ( $\Delta{v}\,$ ). In both cases it is equal to the acceleration (vector or scalar) integrated over time:

$\Delta \mathbf{v} = \mathbf{v}_1 - \mathbf{v}_0 = \int^{t_1}_{t_0} \mathbf {a} \, dt$ (vector version)

$\Delta{v} = {v}_1 - {v}_0 = \int^{t_1}_{t_0} {a} \, dt$ (scalar version)

where:

$\mathbf{v_0}\,$ or ${v_0}\,$ is initial velocity vector or scalar at time $t_0\,$ ,
$\mathbf{v_1}\,$ or ${v_1}\,$ is target velocity vector or scalar at time $t_1\,$ .