Originally Posted by

**skeeter** your title is misleading ... x is defined in terms of a single variable, t

so i got the second derivative equaling

c^2t(-1/2(b^2+c^2t)^-3/2*2c^2t)+(b^2+c^2t^2)^-1/2*c^2dx/dt

is that right? and how do i show that the particle always moves in a positive direction?

chain rule ...

$\displaystyle \frac{dx}{dt} = \frac{1}{2}(b^2+c^2t^2)^{-\frac{1}{2}} \cdot 2c^2 t$

clean up the algebra and use the quotient/chain rule to find $\displaystyle \frac{d^2x}{dt^2}$

note that $\displaystyle \frac{dx}{dt}$ > 0 for $\displaystyle t > 0$