Let's say my ship's velocity during deacceleration phase is given by:

v(t) = v0 * exp(-k * t)

where 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:

• v0
• 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.

Let's say my ship's velocity during deceleration phase is given by: $$ v(t) = v_0 \exp(-k t) $$

where $v_0$ is the speed at the time of starting deceleration 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 $v_f$) at the target position given the initial velocity, $v_0$, and distance to the target, $d_0$?

Or alternatively: given $k$ calculating a distance at which deceleration should start?

I'm making a space simulation game where the ship's warp drive needs to accelerate/decelerate exponentially. While accelerating to a maximum speed is easy the problem is with decelerating so that the ship "stops" at the destination.