it is the decrease of the speed. Of course gravity and drag also accelerate the vehicle, and they can add or subtract to the change in velocity experienced by the vehicle. Hence delta-v may not always be the actual change in speed or velocity of the vehicle. Other derivations Impulse-based The equation can also be derived from the basic integral of acceleration in the form of force (thrust) over mass. By representing the delta-v equation as the following: where T is thrust, is the initial (wet) mass and is the initial mass minus the final (dry) mass, and realising that the integral of a resultant force over time is total impulse, assuming thrust is the only force involved, The integral is found to be: Realising that impulse over the change in mass is equivalent to force over propellant mass flow rate (p), which is itself equivalent to exhaust velocity, the integral can be equated to Acceleration-based Imagine a rocket at rest in space with no forces exerted on it (Newton's First Law of Motion). From the moment its engine is started (clock set to 0) the rocket expels gas mass at a constant mass flow rate R (kg/s) and at exhaust velocity relative to the rocket ve (m/s). This creates a constant force F propelling the rocket that is equal to R × ve. The rocket is subject to a constant force, but its total mass is decreasing steadily because it is expelling gas. According to Newton's Second Law of Motion, its acceleration at any time t is its propelling force F divided by its current mass m: Now, the mass of fuel the rocket initially has on board is equal to m0 – mf. For the constant mass flow rate R it will therefore take a time T = (m0 – mf)/R to burn all this fuel. Integrating both sides of the equation with respect to time from 0 to T (and noting that R = dm/dt allows a substitution on the right), we obtain Limit of finite mass "pellet" expulsion The rocket equation can also be derived as the limiting case of the speed change for a rocket that expels its fuel in the form of pellets consecutively, as , with an effective exhaust speed such that the mechanical energy gained per unit fuel mass is given by . In the rocket's center-of-mass frame, if a pellet of