How Can a Train Travel 1km Optimally by Accelerating and Braking?

[philok]

Homework Statement

A commuter travels between two stations. the stations are only 1.00km apart which means the train never reaches maximum crusing speed. The engineer minimizes the time interval (delta t) between the two stations by accelerating for a time interval (delta t sub 1) at a rate (a sub 1 ) = 0.100 m/s^2 and then immediately braking with acceleration (a sub 2) = -0.500 m/s^2 for a time interval (delta t sub 2).
Find the minimum time interval of travel ( delta t) and the time interval (delta t sub 1).

Homework Equations

The only equations i know are the kinematic equations but I am not sure how to apply them to this question

The Attempt at a Solution

 

[Chewy0087]

Come on, what have you tried so far?

Here's a starter, call the distance he covers whilst accelerating $$D_{1}$$, the distance he covers whilst decelerating $$D_{2}$$. You also know the acceleration of the train while accelerating and decelerating. What can you say about $$D_{1} + D_{2}$$ ? Try writing out the equations and see if you can get unknowns to cancel.