Farmer Maths

A particle moves along a line according to the equation $$(t+1)v^2 a + v^3 = (t+1) v^4 \ln(5t+1)$$ where $a,v,t$ are its acceleration and deceleration and time elapsed (in seconds) from the start of the movement of the particle respectively.
(a) Given that the particle's initial velocity is $\dfrac{5}{76} ms^{-1}$, find the particular solution for $v$.
(b) State $\lim_{t \rightarrow \infty} \dfrac{1}{v}$ and hence comment on whether this model is reasonable.