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:

$\mathrm{\Delta }\mathbf{𝐯}={\mathbf{𝐯}}_1-{\mathbf{𝐯}}_0=\underset{t_0}{\overset{t_1}{\int }}\mathbf{𝐚}dt$ (vector version)

$\mathrm{\Delta }v=v_1-v_0=\underset{t_0}{\overset{t_1}{\int }}adt$ (scalar version)

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

$\mathrm{\Delta }\mathbf{𝐯}={\mathbf{𝐯}}_1-{\mathbf{𝐯}}_0=\mathbf{𝐚}*(t_1-t_0)$

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 :$\mathrm{\Delta }\mathbf{𝐩}=m\mathrm{\Delta }\mathbf{𝐯}$, where $\mathbf{𝐩}$ is momentum and m is mass.