Vt = Vmax * (1 - e^(-t * 10^6 / (I*M) )
Where:
Vt = Velocity after time "t", metres per second.
Vmax = Maximum velocity (top speed), metres per second.
e = Mathematical constant (base of the 'Natural logarithm' - ln).
t = Time, seconds.
I = Inertia Modifier, dimensionless.
M = Mass, kilogrammes.
It can also be written as:
T = I*M * 10^-6 * -ln (1 - Vt / Vmax)
Where:
T = Period to reach Vt, seconds.
I = Inertial Modifier, dimensionless.
ln = Standard mathematical function, Natural logarithm.
Vt = Target velocity, metres per second.
Vmax = Maximum velocity, metres per second.