Editing Delta-v (section)

==Specific cases==
In the absence of external forces:
<math display="block">\Delta{v} = \int_{t_0}^{t_1} \left|\dot{v}\right|\, dt</math>
where <math>\dot{v}</math> is the coordinate acceleration.

When thrust is applied in a constant direction ({{math|{{sfrac|{{var|v}}|{{!}}{{var|v}}{{!}}}}}} is constant) this simplifies to:
<math display="block">\Delta{v} = | v_1 - v_0 |</math>
which is simply the magnitude of the [[Delta-v (physics)|change in velocity]]. However, this relation does not hold in the general case: if, for instance, a constant, unidirectional acceleration is reversed after {{math|({{var|t}}{{sub|1}} − {{var|t}}{{sub|0}})/2}} then the velocity difference is 0, but delta-''v'' is the same as for the non-reversed thrust.

For rockets, "absence of external forces" is taken to mean the absence of gravity drag and atmospheric drag, as well as the absence of aerostatic back pressure on the nozzle, and hence the [[Rocket engine#Vacuum specific impulse, Isp|vacuum I{{sub|sp}}]] is used for calculating the vehicle's delta-''v'' capacity via the [[rocket equation]]. In addition, the costs for [[Atmospheric drag|atmospheric]] losses and [[gravity drag]] are added into the [[delta-v budget|delta-''v'' budget]] when dealing with launches from a planetary surface.<ref>{{Cite book|last1=Sarigul-Klijn|first1=Nesrin|last2=Noel|first2=Chris|last3=Sarigul-Klijn|first3=Martinus|date=2004-01-05|title=Air Launching Eart-to-Orbit Vehicles: Delta V gains from Launch Conditions and Vehicle Aerodynamics|url=https://www.researchgate.net/publication/268564872|doi=10.2514/6.2004-872|isbn=9781624100789}}</ref>