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## Homework Statement

A car and a train move together along straight, parallel paths with the same constant cruising speed v[itex]_{0}[/itex] . At t = 0 the car driver notices a red light ahead and slows down with constant acceleration -a[itex]_{0}[/itex]. Just as the car comes to a full stop, the light immediately turns green, and the car then accelerates back to its original speed v[itex]_{0}[/itex] with constant acceleration a[itex]_{a}[/itex]. During the same time interval, the train continues to travel at the constant speed v[itex]_{0}[/itex] .

What is the distance traveled by the train during the entire period of (negative and positive) acceleration of the car? Expressed in terms of v[itex]_{0}[/itex] and a[itex]_{0}[/itex] .

I already know the answer is d[itex]_{train}[/itex] = [itex]\frac{2(v_{0}^{2})}{a_{0}}[/itex]

However, I'm still trying to figure out why that is the answer.

## Homework Equations

Contant Acceleration Forumula: I believe the relevant equation would be v[itex]_{x^{2}}[/itex]=v[itex]_{0^{2}}[/itex]+2a[itex]_{0}[/itex](x-x[itex]_{0})[/itex]

## The Attempt at a Solution

So far I have total time car was accelerating/decelerating: [itex]\frac{v_{0}}{a_{0}}[/itex] + [itex]\frac{v_{0}}{a_{0}}[/itex] = [itex]\frac{2v_{0}}{a_{0}}[/itex]

Now, if I could just figure out how to get this formula: d[itex]_{train}[/itex] = [itex]\frac{2(v_{0}^{2})}{a_{0}}[/itex]