Delta-v (physics)

For the special astrodynamical meaning, see Delta-v.

In general physics, delta-v is simply a change in velocity. The Greek uppercase letter 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 (Δv). In either case 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:

• v₀ or v₀ is initial velocity (at time t₀),
• v₁ or v₁ is subsequent velocity (at time t₁).

Change in velocity is useful in many cases, such as determining the change in momentum, where :$\Delta{\mathbf{p}} = m\Delta{\mathbf{v}}$, where ,$\mathbf{p}$ is momentum and m is mass.