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)

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

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

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