Okay what am I doing wrong? This is the way I've been doing math for the last two years. This is annoying me. Unless I've been doing everything wrong the last two years, I feel this is correct. I realize it's most likely wrong. Someone please explain to me what I am doing wrong and more important(adsbygoogle = window.adsbygoogle || []).push({}); why.

F = -be^(-a*v) = m dv/dt, a and b are constants.

m [inte]_{vo}^{v}e^(a*v) dv = -b [inte]_{to=0}^{t}dt

m/a e^(a(v - v_{o})) = -b*t

ln[e^(a(v - v_{o}))] = ln[-abt/m]

a(v - v_{o}) = ln[-abt/m]

v(t) = 1/a ln[-abt/m] + v_{o}

dx/dt = v(t) = 1/a ln[-abt/m] + v_{o}

[inte]_{xo=o}^{x}dx = [inte]_{to=o}^{t}1/a ln[-abt/m] + v_{o}dt

x(t) = t/a[ln(-a*b*t/m) + a*v_{o}-1]

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# The Starship Enterprise (variable acceleration problem) part II

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