Question

given initial velocity and acceleration as a function of velocity find velocity time function

Answer 1

So I understand that utilizing a(v) = dv/dt you come out with dt = dv/a(v) and integrate both sides. However if the given acceleration is -v^2 for instance, you would come out with 1/v and if v0 = .4 then you would be left with 1 / v(t) - 1/.4 = t my problem is what happens if you have a(v) = -v^4 and v- = .4 ? I think I may be missing a step in evaluation.

Answer 2

** if you have a(v) = -v^4 and v= .4 ? **
\[ \frac{dv}{dt} = - v^4 \\ -v^{-4} \ dv = dt \\ \frac{1}{3}v^{-3} + C = t \]
initial velocity at t=0 is 0.4
put in t=0 and V= 0.4 and solve for C:
\[ \frac{1}{3\cdot 0.4^3} + C = 0 \\ C= -0.192 \]

Answer 3

yeah my math was poor and I didn't realize it.