EVE's physics engine is based on a 'fluid dynamics model' which assumes that 'space' has some substance to it and thus some friction, this means that with the ship engine turned off you will decelerate, ultimately to a standstill.
How do ships in EVE accelerate and decelerate?
When a ship starts to accelerate it will quickly increase its speed but as the speed increases the acceleration decreases exponentially which means that, in theory, the ship will never reach its top speed. In reality however, it won't take long to get so close to top speed that the difference is negligible and EVE rounds up the figure on your display.
Deceleration is simply acceleration in a direction opposed to the one you are travelling in, i.e. 'braking'. The closer to your top speed you are the faster you will decelerate.
What decides how quickly a ship accelerates?
There are two attributes which determine how quickly a ship accelerates; Mass and Inertial Modifier, the later can be reduced with both skills and modules while mass can never be reduced only increased. The product of Mass and the Inertia Modifier gives the ship's agility which determines how quickly the ship accelerates (and thus how quickly it turns); lower values imply better acceleration and turning speed.
Two ships with identical Mass and Inertial Modifier but different top speeds will reach their respective top speeds in the same period. Thus, a ship with a higher top speed will have a higher acceleration in ms^-2 but will take the same time to reach the speed required to use warp engines.
The following formula describes the velocity of a ship accelerating from a standstill after a particular time:
Explanation: The term after the multiplication sign is the fraction of maximum velocity which is reached in time t. Note that this depends only on time, inertia modifier and mass (e is a constant). This is multiplied by the maximum velocity to find the actual velocity at time t.
The 106 term cancels out a factor of one million in the mass term. So to simplify you can ignore the 106 and use the mass of the ship in millions of kg instead of kg.
As for acceleration itself, this is just the first derivative of velocity with respect to time.
Rearranging the formula for t we arrive at the formula for time taken to accelerate from zero to V:
where tV is the time to accelerate to velocity V in seconds. Note that at V = Vmax, 1 - V / Vmax = 0, but ln 0 is undefined, so in theory it takes infinite time to reach maximum speed (technically, the limit of tV as V approaches Vmax is positive infinity). In practice the game simulation is not perfectly accurate and it actually takes finite time to reach maximum speed to within whatever precision the simulation uses.
Example: Pete has just got himself a new freighter, a Charon.
Time to Warp = 0.02176875 × 1.2 × 109 × 10-6 × -ln (1 - 0.75 / 1) = 0.02176875 × 1.2 × 103 × -ln (1 - 0.75) = 0.02176875 × 1200 × -ln 0.25 = 26.1225 × 1.38629436 = 36.2134744 seconds.
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