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## Homework Statement

There are two train stations, 2.5km (2500m) apart, therefore an ordinary suburban train cannot reach its max v between the two station. They try to minimise time taken by accelerating at a constant rate of 0.1ms

^{-2}for time t

_{1}and decelerate at 0.5ms

^{-2}for time t

_{2}.

Find the maximum speed of the train, and the minimum time taken to travel this distance.[/B]

## Homework Equations

a = v/t

v = d/t

v

_{f}= v

_{i}+ 2ad

## The Attempt at a Solution

I'm not so much stuck on the side of figuring out max velocity and time, I for some reason can not for the life of me figure out how I'm supposed to determine the DISTANCE it takes to reach the max speed.

I know the ratio of acceleration is 1:5, but can't figure out how this then relates into the distances required for acceleration and breaking. I'm not after a full answer because this is an assignment question, but more a poke in the right direction.

Thank you