Physics:Delta-v

For a more in depth astrodynamical definition, see Delta-v.

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 (Δv). In either case it is equal to the acceleration (vector or scalar) integrated over time:

[math]\displaystyle{ \Delta \mathbf{v} = \mathbf{v}_1 - \mathbf{v}_0 = \int^{t_1}_{t_0} \mathbf {a} \, dt }[/math] (vector version)

[math]\displaystyle{ \Delta{v} = {v}_1 - {v}_0 = \int^{t_1}_{t_0} {a} \, dt }[/math] (scalar version)

If acceleration is constant, the change in velocity can thus be expressed as:

[math]\displaystyle{ \Delta \mathbf{v} = \mathbf{v}_1 - \mathbf{v}_0 = \mathbf {a} * (t_1-t_0) }[/math]

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 (impulse), where :[math]\displaystyle{ \Delta{\mathbf{p}} = m\Delta{\mathbf{v}} }[/math], where [math]\displaystyle{ \mathbf{p} }[/math] is momentum and m is mass.