Question

A commuter train travels between two stations by accelerating at the rate a for a time t1 and then slowing down with a negative acceleration of -5a for a time t2. The two stations are a distance d apart and the train never reaches its maximum speed. The train stops at each station. Find times t1 and t2.

Answer 1

I'm also not allowed to use any other equation except these:
\[v^{\rightarrow}=\frac{dr^{\rightarrow}}{dt}\]
\[a^{\rightarrow}=\frac{dv^{\rightarrow}}{dt}\]
\[v^{\rightarrow}=v _{0}^{\rightarrow}+at^{\rightarrow}\]
\[r^{\rightarrow}=r _{0}^{\rightarrow}+v _{0}^{\rightarrow}t+\frac{1}{2}a^{\rightarrow}t^{2}\]