Delta-v (physics)

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

• Vector version: <math display="block">\Delta \mathbf{v} = \mathbf{v}_1 - \mathbf{v}_0 = \int^{t_1}_{t_0} \mathbf {a} \, dt</math>
• Scalar version: <math display="block">\Delta v = {v}_1 - {v}_0 = \int^{t_1}_{t_0} a \, dt</math>

If acceleration is constant, the change in velocity can thus be expressed as: <math dislay="block">\Delta \mathbf{v} = \mathbf{v}_1 - \mathbf{v}_0 = \mathbf{a} \times \Delta t = \mathbf{a} \times (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>\Delta \mathbf{p} = m \Delta \mathbf{v}</math>, where <math>\mathbf{p}</math> is momentum and m is mass.