Let's say my ship's velocity during deacceleration phase is given by:
v(t) = v0 * exp(-k * t)
v0 is the speed at the time of starting deacceleration and
k is arbitrary constant.
My problem is: Is it possible to calculate such
k that the ship "stops" (let's say slows to a velocity
vf) at the target position given:
- distance to the target d0 ?
Or alternatively: given
k calculating a distance at which deacceleration should start?
I'm making a space simulation game where the ship's warp drive needs to accelerate/deaccelerate exponentially. While accelerating to a maximum speed is easy the problem is with deaccelerating so that the ship "stops" at the destination.
Thank you in advance for any help.