I am trying to solve the following
For $q\in\Bbb R$, write $\ddot q = 1$ as a first-order system, find the flow $\Phi_t:\Bbb R^2 \to \Bbb R^2$, and verify that $\Phi_t\circ\Phi_s = \Phi_{t+s}$.
So far i have set $$ u = \frac{dq}{dt} \\u' = u\frac{du}{dt} = 1$$
I have tried to solve this for q and to then set the flow at $\Phi = q(t,q_0)$.
I am not sure if i am going about this correctly, would appreciate some advice on how to proceed.