Velocity and acceleration with velocity degradation

[Narf the Mouse]

Maneuvering a spaceship using just Newtonian equations is a bit much for the average gamer. Therefore, most space-based first-person games use some form of "semi-Newtonian" motion. For example, reducing velocity by Velocity * 0.X per T = 1.

So, using my limited math to factor that:

Normal: V = A * T
Semi: V = (A * T) - ((A * T) * N), where N = V * (1 - ((1 - X) ^ T))
Semi, full: V = (A * T) - ((A * T) * (1 - ((1 - X) ^ T))

With values: A = 5, T = 3.5, X = 0.5

V = (5 * 3.5) - ((5 * 3.5) * (1 - ((1 - 0.5) ^ 3.5))

V = (17.5) - ((17.5) * (1 - ((0.5) ^ 3.5))

V = 17.5 - (17.5 * (1 - 0.0883~))

V = 17.5 - (17.5 * 0.9116~)

V = 17.5 - (15.9532~)

V = 1.5468~


Is this correct, so far? Thanks.

 

[Narf the Mouse]

Can I get help, please? This isn't homework, unless you count self-set homework. All I need is confirmation that I'm resolving this correctly. I rather think I did, but a second opinion on this would be good.The eventual goal is to use Algebrator to resolve to the "chase" polynomial equation, where one semi-Newtonian object "chases" another. And yeah, it'll probably be a quintic or hexic, but I've got a brute-force approximation solver that needs testing.