Delta-v (physics)

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:

$\Delta {\mathbf {v}}={\mathbf {v}}_{1}-{\mathbf {v}}_{0}=\int _{{t_{0}}}^{{t_{1}}}{\mathbf {a}}\,dt$ (vector version)

$\Delta {v}={v}_{1}-{v}_{0}=\int _{{t_{0}}}^{{t_{1}}}{a}\,dt$ (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.