thanks, the 4th line should be [tex]\frac{dv}{dt}[/tex]= [tex]\frac{450v}{(3+s)^2}[/tex]

am not sure what sub. get rid of v.
but v' will give me a instead of v, but is that possible, i mean, if i want to get V' i will have to take thderivative for the whole thing.

your expression for a is correct, but it contains a 'v'. in order to express a completely in terms of s, you need to use the equation [tex]v=\frac{150s}{3+s}[/tex] and plug this into your equation for a.