I'm stuck on this question. Originally part of a mechanics question concerning a trains's motion.
I'm finding the time taken for a train to go from $75\textrm{km/hr}$ to $175\textrm{km/hr}$
The train weighs $300T$, $\textrm{Tractive Effort}= C/v$ in $N$
$\textrm{Resistance} = 4750+kv^2$
Where $C= 2.60M$ and $k=13.3$
$T-R=ma$
$C/v-4750-kv^2=ma$
$C/(\frac{\mathrm dx}{\mathrm dt}) -4750 -k(\frac{\mathrm dx}{\mathrm dt})^2 = m\frac{\mathrm d^2x}{\mathrm dx^2}$
I need to solve for $t$ from $\frac{\mathrm dx}{\mathrm dt}=75$ to $\frac{\mathrm dx}{\mathrm dt}=175$. How do I solve for $t$?
Help appreciated!