Delta-v (physics)

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: $$\Delta \mathbf{v} = \mathbf{v}_1 - \mathbf{v}_0 = \int^{t_1}_{t_0} \mathbf {a} \, dt$$
 * Scalar version: $$\Delta v = {v}_1 - {v}_0 = \int^{t_1}_{t_0} a \, dt$$

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

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.