That sounds about right; the distance should be kept in their though just in case:
C(v)*d/v = d*160/v + d*v^2/100
But yes, you can easily prove that the distance is negligible, meaning that the optimal velocity is the same for all distances.
The function you present has no minimum value due to the fact that it is cubic with no other terms. You can use calculus as follows to prove this:
C(v) = 160 + .01 * v^3
C’(v) = .03 * v^2
0 = .03 * v^2
v^2 = 0 / .03 = 0
v = ±0 = 0
The function C'(v) is the derivative of the cost function. By...