After few years my math skills got a bit rusty and I don't seem to remember how to classify and solve a problem I'm lookin at.
I have four equations and four variables:
$a_xt^2 +At + B=0$
$a_yt^2 +Ct + D=0$
$a_zt^2 +Et + F=0$
$a_x^2 + a_y^2 + a_z^2 = G$
The variables are: $a_x,a_y,a_z,t$ and $t >0$
In short it's an equation that calculates acceleration vector in certain motion during time t. I know the magnitude of the acceleration vector but I want to know how to distribute the components and how long will this motion take. If time t is known the problem becomes trivial. The biggest challenge comes from fact that a is time dependent, $a(t)$.
Could anyone point me in a direction? What problem I'm looking at and whether it's solvable analytically ? If not what numerical method I should use?
At least a gentle poke in the right direction would be much appreciated.