Question: When an object travels through a certain resisting medium the deceleration is proportional to the 4th of the velocity. This, a = -kv^4. Prove v = u(ktu^3 + 1)^1/3 and subsequently x = (1/2ku^2)((ktu^3 + 1)^2/3 - 1). v at time 0 = u and x at time 0 = 0. Equations: Differentiation and integration. Attempt at solution: I've proved the first part, for v. I keep getting (1/6ku)((ktu^3 + 1)^2/3 - 1) for c though. So, not too far out. It should just be a simple u substitution following on from the derivation of v. Could anyone walk through the second part? I have no clue where I'm making the mistake.